# How do you simplify sqrt15 times sqrt21?

Aug 25, 2016

$3 \sqrt{35}$

#### Explanation:

When multiplying 2 square roots they can be combined into one.
Write each number as the product of its prime factors.

sqrt15 xxsqrt 21 = sqrt(5xx3xx3xx7

=$3 \sqrt{35}$

Aug 25, 2016

$3 \sqrt{35}$

#### Explanation:

When simplifying roots of natural numbers is is often useful to first express the numbers as the product of prime numbers.

Consider: $15 = 3 \times 5$ and $21 = 3 \times 7$

Also: $\sqrt{15} \times \sqrt{21} = \sqrt{15 \times 21}$

$= \sqrt{3 \times 5 \times 3 \times 7}$

$= 3 \sqrt{5 \times 7} = 3 \sqrt{35}$

Aug 25, 2016

Same thing but with a slight twist in approach

$3 \sqrt{35}$

#### Explanation:

Look for common factors. Notice that 3 will divide into both 15 and 21 with no remainder.

Write as:$\text{ } \sqrt{3 \times 5} \times \sqrt{3 \times 7}$

You can split these in the following way:

$\sqrt{3} \times \sqrt{5} \times \sqrt{3} \times \sqrt{7}$

But ${\left(\sqrt{3}\right)}^{2} = 3$ giving:

$3 \left(\sqrt{5} \times \sqrt{7}\right)$

But $\sqrt{5} \times \sqrt{7}$ is the same thing as $\sqrt{5 \times 7} = \sqrt{35}$

$3 \sqrt{35}$