Question

simplify. (sqrt{28}+2sqrt{63})

Explanation:

Step1: Simplify square - roots separately

Simplify $\sqrt{28}$ and $\sqrt{63}$.
We know that $28 = 4\times7$, so $\sqrt{28}=\sqrt{4\times7}=\sqrt{4}\times\sqrt{7}=2\sqrt{7}$.
And $63 = 9\times7$, so $\sqrt{63}=\sqrt{9\times7}=\sqrt{9}\times\sqrt{7}=3\sqrt{7}$.

Step2: Substitute simplified square - roots

The original expression $\sqrt{28}+2\sqrt{63}$ becomes $2\sqrt{7}+2\times3\sqrt{7}$.

Step3: Perform multiplication

$2\times3\sqrt{7}=6\sqrt{7}$, so the expression is $2\sqrt{7}+6\sqrt{7}$.

Step4: Combine like terms

Since the terms have the same radical part $\sqrt{7}$, we can add the coefficients: $(2 + 6)\sqrt{7}=8\sqrt{7}$.

Answer:

$8\sqrt{7}$