Question

Simplify 4 root 18/ root 12- 8 root 75/ root 32+9 root 2/root 3

Answer 1

Answer:

answer of this question is zero

Answer 2

The correct answer is 0.

Given: The equation = $\frac{4\sqrt{18} }{\sqrt{12} } -\frac{8\sqrt{75} }{\sqrt{32} } +\frac{9\sqrt{2} }{\sqrt{3} }$.

To Find: Simplify the equation.

Solution:

$\frac{4\sqrt{18} }{\sqrt{12} } -\frac{8\sqrt{75} }{\sqrt{32} } +\frac{9\sqrt{2} }{\sqrt{3} }$

Firstly solve first term $\frac{4\sqrt{18} }{\sqrt{12} }$.

$\frac{4\sqrt{18} }{\sqrt{12} }=\frac{4\sqrt{2*3*3} }{\sqrt{2*2*3} }$ = $\frac{12\sqrt{2} }{2\sqrt{3} }$ = $\frac{6\sqrt{2} }{\sqrt{3} }$

Multiply and divide by $\sqrt{3}$ to rationalize denominator.

$\frac{6\sqrt{2} }{\sqrt{3} }*\frac{\sqrt{3} }{\sqrt{3} }$ = $\frac{6\sqrt{6} }{3}$ = $2\sqrt{6}$

Now take second term $\frac{8\sqrt{75} }{\sqrt{32} }$.

$\frac{8\sqrt{75} }{\sqrt{32} }=\frac{8\sqrt{3*5*5} }{\sqrt{4*4*2} } =\frac{40\sqrt{3} }{4\sqrt{2} } =\frac{10\sqrt{3} }{\sqrt{2} }$

Multiply and divide by $\sqrt{2}$ to rationalize denominator.

$\frac{10\sqrt{3} }{\sqrt{2} }*\frac{\sqrt{2} }{\sqrt{2} }$ = $5\sqrt{6}$

Now take third term $\frac{9\sqrt{2} }{\sqrt{3} }$.

Multiply and divide by $\sqrt{3}$ to rationalize denominator.

$\frac{9\sqrt{2} }{\sqrt{3} }*\frac{\sqrt{3} }{\sqrt{3} }$ = $3\sqrt{6}$

Now put all three in the equation.

$2\sqrt{6}-5\sqrt{6} +3\sqrt{6}$

= 0

Hence, the answer is 0.

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