1 Marks Question

Question 511 Mark

There are __________ perfect squares between $1$ and $100.$

Answer

There are $8$ perfect squares between $1$ and $100.$
Solution:
There are $8$ perfect squares between $1$ and $100,$ i.e. $4, 9, 16, 25, 36, 49, 64$ and $81.$

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Question 521 Mark

The least number by which $125$ be multiplied to make it a perfect square is ___________.

Answer

The least number by which $125$ be multiplied to make it a perfect square is $5.$
Solution: $\begin{array}{c|c}5&125\\\hline5&25\\\hline5&5\\\hline&1\end{array}$ Resolving $125$ into prime factors, we get $125 = 5 \times 5 \times 5$ Grouping the factors in triplets of equal factors, we get $125 = (5 \times 5) \times 5$ We observe that $5$ is without a pair. Thus, we must multiply the number by $5,$ so that the product is a perfect square. Hence, the least number, which should be multiplied with $125$ to make it a perfect square, is $5.$

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Question 531 Mark

Find the square root of $324$ by the method of repeated subtraction.

Answer

Since, the first three multiples of $3$ are $3, 6$ and $9.$
Hence, the cubes of first three multiples of $3$ are $(3)^3, (6)^3$ and $(9)^3$, i.e. $27, 216$ and $729.$

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MATHS 1 Marks Question