# How do you simplify sqrt8*sqrt10?

Nov 21, 2017

Arrange the equation and get $4 \sqrt{5}$

#### Explanation:

$\sqrt{8} \times \sqrt{10} = \sqrt{80}$ under one square root. Further,

$= \sqrt{16 \times 5} = 4 \sqrt{5}$

This is the shortest form. Your answer is $4 \sqrt{5}$

Nov 21, 2017

sqrt8sqrt10=color(blue)(4sqrt5

#### Explanation:

Simplify:

$\sqrt{8} \sqrt{10}$

Prime factorize $8$.

$\sqrt{\left(2 \times 2\right) \times 2} \cdot \sqrt{10}$

$2 \sqrt{2} \cdot \sqrt{10}$

$2 \sqrt{2 \times 10}$

$2 \sqrt{20}$

Prime factorize $20$.

$2 \sqrt{\left(2 \times 2\right) \times 5}$

Simplify.

$2 \times 2 \sqrt{5}$

Simplify.

$4 \sqrt{5}$

Nov 21, 2017

$4 \sqrt{5}$

#### Explanation:

you know that when multiplying roots they can go 'in each other' thus:
$\sqrt{8} \cdot \sqrt{10}$ = $\sqrt{8 \cdot 10}$

then break down each number to it's primary numbers

$\sqrt{\left(2 \cdot 2 \cdot 2\right) \cdot \left(2 \cdot 5\right)}$

notice that we have numbers that are repeated twice (because here we have a square root)
$\sqrt{\left(2 \cdot 2\right) \cdot \left(2 \cdot 2\right) \cdot 5}$

then take them out of the square root. I took them out one at a time.
$2 \sqrt{\left(2 \cdot 2\right) \cdot 5}$
Note that when you take them out you put only one repeated term

take the second 2 out and remember this is all multiplication so 2 is multiplied by the 2 in front of the square root.

$\left(2 \cdot 2\right) \sqrt{5}$

the $\sqrt{5}$ cannot be simplified, so we leave it as it is. (there is not a whole numbers that we can multiply by itself to get 5 )

so we are left with just simplifying the front $2 \cdot 2 = 4$ thus

$4 \sqrt{5}$

Note: this could be also solved as:
$\sqrt{\left(2 \cdot 2\right) \cdot \left(2 \cdot 2\right) \cdot 5} = \sqrt{4 \cdot 4 \cdot 5}$
thus 4 will be our repeated twice number, then we simply would take it out to get :
$4 \sqrt{5}$

The second way would be more useful when dealing with larger numbers.

I hope this helps. thank you.