1 Marks Question

Question 511 Mark

What will be the units digit of the squares of the following numbers?
12796

Answer

The units digit is affected only by the last digit of the number. Hence, for each question, we only need to examine the square of its last digit. Its last digit is 6. Hence, the units digit is the last digit of 36 (36 = 6²), which is 6.

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Question 521 Mark

Using square root table, find the square root,
$\frac{99}{144}$

Answer

$\sqrt{\frac{99}{144}}=\frac{\sqrt{3\times3\times11}}{\sqrt{144}}$
$=\frac{3\sqrt{11}}{12}$
$=\frac{3\times3.3166}{12}$ $\big($Using the square root table to find $\sqrt{11}\big)$
$=0.829$

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Question 531 Mark

Using square root table, find the square root,
$\frac{57}{169}$

Answer

$\sqrt{\frac{57}{169}}=\frac{\sqrt{3}\times\sqrt{19}}{\sqrt{169}}$
$=\frac{1.732\times4.3589}{13}$ $\big($ Using the square root table to find $\sqrt{3}$ and $\sqrt{19}\big)$
$=0.581$

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Question 541 Mark

Using square root table, find the square root:
8700

Answer

Using the table to find $\sqrt{3}$ and $\sqrt{29}$
$\sqrt{8700}=\sqrt{3}\times\sqrt{29}\times\sqrt{100}$
$=1.7321\times5.385\times10$
$=93.27$

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Question 551 Mark

Using square root table, find the square root:
82

Answer

Using the table to find $\sqrt{2}$ and $\sqrt{41}$
$\sqrt{82}=\sqrt{2}\times\sqrt{41}$
$=1.414\times6.403$
$=9.055$

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Question 561 Mark

Using square root table, find the square root:
74

Answer

Using the table to find $\sqrt{2}$ and $\sqrt{37}$
$\sqrt{74}=\sqrt{2}\times\sqrt{37}$
$=1.414\times0.083$
$=8.602$

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Question 571 Mark

Using square root table, find the square root:
7

Answer

From the table, we directly find that the square root of 7 is 2.646

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Question 581 Mark

Using square root table, find the square root:
6929

Answer

Using the table to find $\sqrt{41}$
$\sqrt{6929}=\sqrt{169}\times\sqrt{41}$
$=13\times6.4031$
$=83.239$

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Question 591 Mark

Using square root table, find the square root:
540

Answer

Using the table to find $\sqrt{3}$ and $\sqrt{5}$
$\sqrt{540}=\sqrt{54}\times\sqrt{10}$
$=2\times3\sqrt{3}\times\sqrt{5}$
$=2\times3\times1.732\times2.2361$
$=23.24$

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Question 601 Mark

Using square root table, find the square root:
3509

Answer

Using the table to find $\sqrt{29}$
$\sqrt{3509}=\sqrt{121}\times\sqrt{29}$
$=11\times5.3851$
$=59.235$

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Question 611 Mark

Using square root table, find the square root:
198

Answer

Using the table to find $\sqrt{2}$ and $\sqrt{11}$
$\sqrt{198}=\sqrt{2}\times\sqrt{9}\times\sqrt{11}$
$=1.414\times3\times3.317$
$=14.070$

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Question 621 Mark

Using square root table, find the square root:
15

Answer

Using the table to find $\sqrt{3}$ and $\sqrt{5}$
$\sqrt{15}=\sqrt{3}\times\sqrt{5}$
$=1.732\times2.236$
$=3.873$

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Question 631 Mark

Using square root table, find the square root:
1110

Answer

$\sqrt{1110}=\sqrt{2}\times\sqrt{3}\times\sqrt{5}\times\sqrt{37}$
$=1.414\times1.732\times2.236\times6.083$ (Using the table to find all the square roots)
$=33.312$

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Question 641 Mark

Using square root table, find the square root:
110

Answer

$\sqrt{110}=\sqrt{2}\times\sqrt{5}\times\sqrt{11}$
$=1.414\times2.236\times3.317$ (Using the suare root table to find all the square roots)
$=10.488$

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Question 651 Mark

The following numbers are not perfect squares. Give reason.
i. 1547
ii. 45743
iii. 8948
iv. 333333

Answer

A number ending with 2, 3, 7 or 8 cannot be a perfect square.
i. Its last digit is 7. Hence, 1547 cannot be a perfect square.
ii. Its last digit is 3. Hence, 45743 cannot be a perfect square.
iii. Its last digit is 8. Hence, 8948 cannot be a perfect square.
iv. Its last digit is 3. Hence, 333333 cannot be a perfect square.

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Question 661 Mark

Given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{7}=2.646,$ find the square roots of the following:
$\frac{400}{63}$

Answer

From the given values, we can simplify the expressions in the following manner:
$\sqrt{\frac{400}{63}}=\frac{20}{3\sqrt{7}}$
$=\frac{20}{3\times2.646}=2.520$

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Question 671 Mark

Given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{7}=2.646,$ find the square roots of the following:
$\frac{27}{50}$

Answer

From the given values, we can simplify the expressions in the following manner:
$\sqrt{\frac{27}{50}}=\frac{3\sqrt{3}}{5\sqrt{2}}=\frac{3\times1.732}{5\times1.414}=0.735$

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Question 681 Mark

Given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{7}=2.646,$ find the square roots of the following:
$\frac{256}{5}$

Answer

From the given values, we can simplify the expressions in the following manner:
$\sqrt{\frac{256}{5}}=\frac{16}{\sqrt{5}}=\frac{16}{2.236}=7.155$

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Question 691 Mark

Given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{7}=2.646,$ find the square roots of the following:
$\frac{196}{75}$

Answer

From the given values, we can simplify the expressions in the following manner:
$\sqrt{\frac{196}{75}}=\frac{14}{5\sqrt{3}}$
$=\frac{14}{5\times1.732}=1.617$

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Question 701 Mark

Given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{7}=2.646,$ find the square roots of the following:
$\frac{150}{7}$

Answer

From the given values, we can simplify the expressions in the following manner:
$\sqrt{\frac{150}{7}}=\frac{5\sqrt{2}\times\sqrt{3}}{\sqrt{7}}$
$=\frac{5\times1.414\times1.732}{2.646}=4.628$

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Question 711 Mark

Given that, $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{7}=2.646,$ evaluate each of the following:
$\sqrt{\frac{2500}{3}}$

Answer

Given,
$\sqrt{3}=1.732$
$\sqrt{\frac{2500}{3}}=\frac{\sqrt{2500}}{\sqrt{3}}=\frac{50}{1.732}=28.867$

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Question 721 Mark

Given that, $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{7}=2.646,$ evaluate each of the following:
$\sqrt{\frac{144}{7}}$

Answer

Given,
$\sqrt{7}=2.646$
$\sqrt{\frac{144}{7}}=\frac{\sqrt{144}}{\sqrt{7}}=\frac{12}{2.646}=4.536$

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Question 731 Mark

Find the value of:
$\sqrt{72}\times\sqrt{338}$

Answer

We have,
$\sqrt{72}\times\sqrt{338}=\sqrt{72\times338}$
$=\sqrt{2\times2\times2\times3\times3\times2\times13\times13}$
$=\sqrt{2\times2\times2\times2\times3\times3\times13\times13}$
$=2\times2\times3\times13$
$=156$

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Question 741 Mark

Find the value of:
$\sqrt{45}\times\sqrt{20}$

Answer

We have,
$\sqrt{45}\times\sqrt{20}=\sqrt{3\times3\times5\times2\times2\times5}$
$=\sqrt{3\times3\times2\times2\times5\times5}$

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Question 751 Mark

Find the value of:
$\frac{\sqrt{80}}{\sqrt{405}}$

Answer

We have,
$\frac{\sqrt{80}}{\sqrt{405}}=\sqrt{\frac{80}{405}}$
$=\sqrt{\frac{16}{81}}=\frac{\sqrt{16}}{\sqrt{81}}=\frac{4}{9}$

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Question 761 Mark

By just examining the units digits, can you tell which of the following cannot be whole squares?
i. 1026
ii. 1028
iii. 1024
iv. 1022
v. 1023
vi. 1027

Answer

If the units digit of a number is 2, 3, 7 or 8, the number cannot be a whole square.
i. 1026 has 6 as the units digit, so it is possibly a perfect square.
ii. 1028 has 8 as the units digit, so it cannot be a perfect square.
iii. 1024 has 4 as the units digit, so it is possibly a perfect square.
iv. 1022 has 2 as the units digit, so it cannot be a perfect square.
v. 1023 has 3 as the units digit, so it cannot be a perfect square.
vi. 1027 has 7 as the unit digit, so it cannot be a perfect square.
Hence, by examining the units digits, we can be certain that 1028, 1022, 1023 and 1027 cannot be whole squares.

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MATHS 1 Marks Question