Question

3√7 +7✓63 - ✓7

3 root 7 +7 root 63 - root 7

simple form​

Answer 1

Answer:

3√7 +7✓63 - ✓7

= 169√7/7

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Answer 2

Answer:

After simplification value of the given term is$23 \sqrt{7} .$

Step-by-step explanation:

Given,$3 \sqrt{7} + 7 \sqrt{63} - \sqrt{7}$

This is a problem of power indices.

$= 3 \sqrt{7} - \sqrt{7} + 7 \sqrt{63}$

$= 2 \sqrt{7} + 7 \sqrt{63}$

Now,$63 = 3 \times 3 \times 7$

$= 2 \sqrt{7} + 7 \sqrt{3 \times 3 \times 7} = 2 \sqrt{7} + 7 \times 3 \sqrt{7} = 2 \sqrt{7} + 21 \sqrt{7} = 23 \sqrt{7}$

Here applied formulas are

$\sqrt{x} + \sqrt{x} = 2 \sqrt{x}$

$\sqrt{x \times x \times y} = x \sqrt{y}$

$y \sqrt{x} - \sqrt{x} = (y - 1) \sqrt{x}$

Some other formulas of power of indices,

$\sqrt{x} = {x}^{ \frac{1}{2} }$

${x}^{ - 1} = \frac{1}{x}$

${x}^{0} = 1$

$\sqrt{x} \times \sqrt{x} = x$

e.t.c.