Question

4√18/√12-8√75/√32+9√2/√3​

Answer 1

Answer:

0

Step-by-step explanation:

4√18/√12-8√75/√32+9√2/√3​=

4*3√2/2√3-8*5√3/4√2+9√2/√3​=

6√2/√3-10√3/√2+9√2/√3=

6​√6/3-10√6/2+9√6/3=

2√6-5√6+3√6=5√6-5√6=0

Answer 2

The answer is 0.

Step-by-step explanation:

According to the given information, the expression is given as, $\frac{4\sqrt{18} }{\sqrt{12} } -\frac{8\sqrt{75} }{\sqrt{32} } +\frac{9\sqrt{2} }{\sqrt{3} } \\=\frac{4\sqrt{2*3*3} }{\sqrt{2*2*3} } -\frac{8\sqrt{5*5*3} }{\sqrt{2*2*2*2*2} } +\frac{9\sqrt{2} }{\sqrt{3} } \\\\=\frac{4\sqrt{3} }{\sqrt{2} } -5\sqrt{6} +\frac{9\sqrt{2} }{\sqrt{3} }\\=2\sqrt{6}-5\sqrt{6} +3\sqrt{6} \\=\sqrt{6}*(2-5+3)\\ =\sqrt{6}*0\\ =0$

Here, clearly when a number is inside the square root, and if the number is a perfect square such as 4 which can be factorized as 2*2, one of the factors of the perfect square is taken out of the square root, and if not, the number stays inside the square root.

In the second line of the process, the numbers inside the square roots are factorized so that it is easier to be cancelled out from the numerator and denominator.

Hence, the answer is 0.

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