Question

adding / subtracting radical expressions
score: 0/2 penalty: 1 off
question
express in simplest radical form.
$5\sqrt{10} + 5\sqrt{160}$
answer attempt 1 out of 2
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Explanation:

Step1: Simplify $\sqrt{160}$

Factor 160: $160 = 16\times10$, so $\sqrt{160}=\sqrt{16\times10}=\sqrt{16}\times\sqrt{10}=4\sqrt{10}$

Step2: Substitute back into the expression

The original expression is $5\sqrt{10} + 5\sqrt{160}$. Substitute $\sqrt{160}=4\sqrt{10}$:
$5\sqrt{10}+5\times4\sqrt{10}=5\sqrt{10}+20\sqrt{10}$

Step3: Combine like terms

Since both terms have $\sqrt{10}$, we add the coefficients: $(5 + 20)\sqrt{10}=25\sqrt{10}$

Answer:

$25\sqrt{10}$