+0

0
658
3
+1280

AWESOMEEE  Jun 30, 2015

#2
+19206
+5

$$\boxed{~~ \text{Formula: } \sqrt[n]{a\cdot b} = \sqrt[n]{a}\cdot \sqrt[n]{b} ~~}$$

$$\root 3 \of {x \root 3 \of {x \root 3 \of {x \sqrt{x}}}} \\\\ = \root 3 \of {x} \cdot \root 3 \of {\root 3 \of {x \root 3 \of {x \sqrt{x}}}}\\\\ = \root 3 \of {x} \cdot \root 9 \of {x \root 3 \of {x \sqrt{x}}}\\\\ = \root 3 \of {x} \cdot \root 9 \of {x} \cdot \root 9 \of {\root 3 \of {x \sqrt{x}}}\\\\ = \root 3 \of {x} \cdot \root 9 \of {x} \cdot \root 27 \of {x \sqrt{x}}\\\\ = \root 3 \of {x} \cdot \root 9 \of {x} \cdot \root 27 \of {x} \cdot \root 27 \of {\sqrt{x}}\\\\ = \root 3 \of {x} \cdot \root 9 \of {x} \cdot \root 27 \of {x} \cdot \root 54 \of {x}\\\\ = x^{\frac13} \cdot x^{\frac19} \cdot x^{\frac1{27}} \cdot x^{\frac1{54}}\\\\ = x^{\frac13+\frac19+\frac1{27}+ \frac1{54}}\\\\ = x^{\frac13 \cdot \frac{18}{18} +\frac19 \cdot \frac{6}{6} +\frac1{27} \cdot \frac{2}{2} + \frac1{54}}\\\\ =x^{\frac{18+6+2+1}{54} } \\\\$$

$$\\=x^{\frac{27}{54}}\\\\ =x^{\frac{1}{2} } \\\\ \mathbf{= \sqrt{x}}$$

heureka  Jul 1, 2015
Sort:

#1
+85624
+5

## √x

Basically, we're taking the cube root of x^(3/2) = x^(1/2) and multiplying this by x  = (x)^(3/2)....then taking the cube root of that, etc.........the last operation results in  (x)^(3/2)^(1/3)  = x^(1/2)  =

## √x

CPhill  Jun 30, 2015
#2
+19206
+5

$$\boxed{~~ \text{Formula: } \sqrt[n]{a\cdot b} = \sqrt[n]{a}\cdot \sqrt[n]{b} ~~}$$

$$\root 3 \of {x \root 3 \of {x \root 3 \of {x \sqrt{x}}}} \\\\ = \root 3 \of {x} \cdot \root 3 \of {\root 3 \of {x \root 3 \of {x \sqrt{x}}}}\\\\ = \root 3 \of {x} \cdot \root 9 \of {x \root 3 \of {x \sqrt{x}}}\\\\ = \root 3 \of {x} \cdot \root 9 \of {x} \cdot \root 9 \of {\root 3 \of {x \sqrt{x}}}\\\\ = \root 3 \of {x} \cdot \root 9 \of {x} \cdot \root 27 \of {x \sqrt{x}}\\\\ = \root 3 \of {x} \cdot \root 9 \of {x} \cdot \root 27 \of {x} \cdot \root 27 \of {\sqrt{x}}\\\\ = \root 3 \of {x} \cdot \root 9 \of {x} \cdot \root 27 \of {x} \cdot \root 54 \of {x}\\\\ = x^{\frac13} \cdot x^{\frac19} \cdot x^{\frac1{27}} \cdot x^{\frac1{54}}\\\\ = x^{\frac13+\frac19+\frac1{27}+ \frac1{54}}\\\\ = x^{\frac13 \cdot \frac{18}{18} +\frac19 \cdot \frac{6}{6} +\frac1{27} \cdot \frac{2}{2} + \frac1{54}}\\\\ =x^{\frac{18+6+2+1}{54} } \\\\$$

$$\\=x^{\frac{27}{54}}\\\\ =x^{\frac{1}{2} } \\\\ \mathbf{= \sqrt{x}}$$

heureka  Jul 1, 2015
#3
+92193
0

You made that look REALLY hard Heureka   LOL   :))

Melody  Jul 2, 2015

### 17 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details