Question

Simplify 4√16 + 8√16

Answer 1

$4\sqrt{16} + 8\sqrt{16}$:

Since $\sqrt{1} =1$, we get:

$4\cdot \:1\cdot \:6+8\cdot \:1\cdot \:6=24+48=72$

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$7\sqrt{4} *3\sqrt{8}$

We have $\sqrt{4}=2$

simplify $\sqrt{8} = \sqrt{2^3} = \sqrt{2^2*2}$

then the radical rule is used: $\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}$

⇒ $\sqrt{2^2*2} = \sqrt{2^2} \sqrt{2}= \sqrt{4}\sqrt{2} =2\sqrt{2}$

Now we have $\sqrt{4}=2$ and $\sqrt{8}=2 \sqrt{2}$

$7\sqrt{4} *3\sqrt{8} = 7*2*3*2\sqrt{2} = 84 \sqrt{2}$

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$2\sqrt{4}+5 \sqrt{9}$

$2\sqrt{4} =2*2= 4$ and $5\sqrt{9} =5*3= 15$

$2\sqrt{4}+5 \sqrt{9} = 4+15 = 19$

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$4\sqrt{5} -2\sqrt{5} = 2\sqrt{5}$

since $2\sqrt{5}$ is the half of $4\sqrt{5}$

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$-4\sqrt{2}\:+\:5\sqrt{2} =1 \sqrt{2} = \sqrt{2}$    (-4+5=1)