Question

Which choice is equivalent to the expression below? 5√10+√40+√90 the answer was 10√10

Answer 1

Answer:

$5\sqrt{10}+\sqrt{40} +\sqrt{90}=10\sqrt{10}$

Step-by-step explanation:

We have the following expression:

$5\sqrt{10}+\sqrt{40} +\sqrt{90}$

Remember the property of root multiplication:

$\sqrt[n]{x*y}=\sqrt[n]{x}\sqrt[n]{y}$

Therefore:

$\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$

Also:

$\sqrt{90}=\sqrt{9*10}=\sqrt{9}*\sqrt{10}=3\sqrt{10}$

Then we have that:

$5\sqrt{10}+\sqrt{40} +\sqrt{90}=5\sqrt{10}+2\sqrt{10}+3\sqrt{10}$

Remember the property of sum of roots:

$a\sqrt{b}+2a\sqrt{b}=3a\sqrt{b}$

Finally:

$5\sqrt{10}+\sqrt{40} +\sqrt{90}=(5+2+3)\sqrt{10}$

$5\sqrt{10}+\sqrt{40} +\sqrt{90}=10\sqrt{10}$