Question

3 root 7 + 7 root 63 + root 7 upon 7

Answer 1

Answer:

$\frac{169 \sqrt{7} }{7}$

Step-by-step explanation:

3

$3 \sqrt{7} + 7 \sqrt{63} + \frac{ \sqrt{7} }{7} \\ = 3 \sqrt{7} + 21 \sqrt{7} + \frac{ \sqrt{7} }{7} \\ = \frac{21 \sqrt{7 } + 147 \sqrt{7} + \sqrt{7} }{7} \\ = \frac{169 \sqrt{7} }{7}$

Answer 2

We need to recall the following rules to solve the equation.

• $\sqrt{a^{2}*b }=a\sqrt{b}$
• $a\sqrt{b} +c\sqrt{b} =(a+c)\sqrt{b}$
• $\frac{\sqrt{a} }{a}=\frac{1}{\sqrt{a} }$
• $\sqrt{a}\sqrt{a}=a$

This problem is about simplifying the square root.

Given:

$3\sqrt{7} + 7\sqrt{63} + \frac{\sqrt{7} }{7}$

$=3\sqrt{7} + 7\sqrt{9*7} + \frac{1}{\sqrt{7} }$

$=3\sqrt{7} + 7*3\sqrt{7} + \frac{1}{\sqrt{7} }$

$=3\sqrt{7} + 21\sqrt{7} + \frac{1}{\sqrt{7} }$

$=24\sqrt{7} + \frac{1}{\sqrt{7} }$

$=\frac{(24\sqrt{7}*\sqrt{7})+1}{\sqrt{7}}$

$=\frac{168+1}{\sqrt{7}}$

$=\frac{169}{\sqrt{7}}$