Question

How do you simplify 9+3√6√3?

Answer 1

Answer : 21.72792

Step by step explanation :

$9 + 3 \sqrt{6} \sqrt{3}$

Calculate the product. The product of the roots with the same index is equal to the root of the product.

$= > 9 + 3 \sqrt{6 \times 3}$

Multiply the numbers

$= > 9 + 3 \sqrt{18}$

Simplify the radicle. Factor out the perfect square

$= > 9 + 3 \sqrt{3 {}^{2} \times 2 }$

The root of a product is equal to the product of the roots of each factor.

$= > 9 + 3 \sqrt{3 {}^{2} } \sqrt{2}$

Reduce the index of the radical and exponent with 2

$= > 9 + 3 \times 3 \sqrt{2}$

Calculate the product

$= > 9 + 9 \sqrt{2}$

$= > 21.72792$