Multiply nine square root of 3 × 6 square root of seven give an exact answer

Answer 1

To multiply the expressions "nine square root of 3" and "6 square root of seven," you can simplify each square root separately and then multiply the resulting numbers together.

First, simplify the square root of 3. Since there are no perfect square factors of 3, the square root of 3 remains as it is: √3.

Next, simplify the square root of seven. There are no perfect square factors of 7 either, so the square root of seven remains: √7.

Now, multiply the numbers: 9 * 6 = 54.

Finally, combine the square roots with the multiplied number: 54√3√7.

However, we can simplify this further. The product of two square roots (√3 * √7) is equal to the square root of their product (√(3 * 7)).

So, 54√3√7 becomes 54√(3 * 7) = 54√21.

Therefore, the exact answer is 54√21.