Question

Square root of 72 multiplied by square root of 98

Answer 1

The value of $\sqrt{72}\times\sqrt{98}$ is 84.

Concept to be used:

In order to solve the problem, we find the square roots of the given numbers by prime factorization. Then use the following rule,

$\sqrt{a\times a\times b\times b}=a\times b$

or, $\sqrt{a^{2}\times b^{2}}=a\times b$

Also, $\boxed{\sqrt{a}\times \sqrt{b}=\sqrt{a\times b}}$

Step-by-step explanation:

Refer to the attached image to find the prime factorization of 72 and 98.

We have

• 72 = 2 × 2 × 2 × 3 × 3 and
• 98 = 2 × 7 × 7

Now, $\sqrt{72}\times \sqrt{98}$

$=\sqrt{72\times 98}$

$=\sqrt{2\times 2\times 2\times 3\times 3\times 2\times 7\times 7}$

$=\sqrt{2\times 2\times 2\times 2\times 3\times 3\times 7\times 7}$

$=\sqrt{2^{2}\times 2^{2}\times 3^{2}\times 7^{2}}$

= 2 × 2 × 3 × 7

= 84

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