Question

`sqrt(8) xx sqrt(64)` is equal to ______.

Options

• 16

• 32

• `16sqrt(2)`

• `32sqrt(2)`

Answer 1

`sqrt(8) xx sqrt(64)` is equal to `underlinebb(16sqrt(2))`.

Explanation:

The value of `sqrt(8) xx sqrt(64)` is

`sqrt(8) xx sqrt(64)`

= `sqrt(8 xx 64)`

= `sqrt(512)`

Now, `sqrt(512)`

= `sqrt(256 xx 2)`

= `sqrt(256) xx sqrt(2)`

= `16sqrt(2)`

When multiplying square roots, you multiply the numbers inside the root and then simplify.

Since 8 × 64 = 512 and 512 can be broken down into 256 × 2, with 256 being a perfect square, we simplify as `16sqrt(2)`.

Hence, `sqrt(8) xx sqrt(64) = 16sqrt(2)`.