Question
Evaluate: $\sqrt{98}\times\sqrt{162}$
✓
Answer
$\sqrt{98}\times\sqrt{162}$
$=\sqrt{98\times162}$
$=\sqrt{2\times7\times7\times2\times3\times3\times3\times3}$
$=\sqrt{\overline{2\times2}\times\overline{7\times7}\times\overline{3\times3}\times\overline{3\times3}}$
$=2\times7\times3\times3$
$=126$
$\begin{array}{c|c}2&98\\\hline7&29\\\hline7&7\\\hline&1\end{array}$
$\begin{array}{c|c}2&162\\\hline3&81\\\hline3&27\\\hline3&9\\\hline3&3\\\hline&1\end{array}$
$=\sqrt{98\times162}$
$=\sqrt{2\times7\times7\times2\times3\times3\times3\times3}$
$=\sqrt{\overline{2\times2}\times\overline{7\times7}\times\overline{3\times3}\times\overline{3\times3}}$
$=2\times7\times3\times3$
$=126$
$\begin{array}{c|c}2&98\\\hline7&29\\\hline7&7\\\hline&1\end{array}$
$\begin{array}{c|c}2&162\\\hline3&81\\\hline3&27\\\hline3&9\\\hline3&3\\\hline&1\end{array}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In a model of a ship, the mast is 9 cm high, while the mast of the actual ship is 12 m high. If the length of the ship is 28 m , how long is the model ship?
If sum of the number $985$ and two other numbers by arranging the digits of $985$ in cyclic order is divided by $111, 22$ and $37$ respectively. Find the quotient in each case.
→If $1AB + CCA = 697$ and there is no carry–over in addition, find the value of $A + B + C.$
→Find the square root of the following correct to three places of decimal: $\frac{7}{8}$
→$11$ men can dig $6\frac{3}{4}$ metre-long trench in one day. How many men should be employed for digging $27$-metre-long trench of the same type in one day?
→Find the following products: $\Big(\text{x}^4+\frac{1}{\text{x}^4})×\Big(\text{x}+\frac{1}{\text{x}}\Big)$
→Subtract the sum of $(2x - x^2+ 5)$ and $(-4x - 3 + 7x^2)$ from $5.$
→Find whether, or not the first polynomial is a factor of the second: $\frac{3\text{z}^2-13\text{z}+4}{4-\text{z}}$
→The adjoining pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, then answer the following questions:
(i) In which subject did the student score 105 marks?
[Hint : for 540 marks, the central angle $=360^{\circ}$.
So, for 105 marks, what is the central angle?]
(ii) How many more marks were obtained by the student in Mathematics than in Hindi?
(iii) Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.
[Hint : Just study the central angles.]
→(i) In which subject did the student score 105 marks?
[Hint : for 540 marks, the central angle $=360^{\circ}$.
So, for 105 marks, what is the central angle?]
(ii) How many more marks were obtained by the student in Mathematics than in Hindi?
(iii) Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.
[Hint : Just study the central angles.]
Check, whether 180 is a perfect square or not using prime factorisation.