Question

Simplify the following surds
√175+√112

Answer 1

Answer:

$\red { \sqrt{175} + \sqrt{112}}\green {=9\sqrt{7}}$

Step-by-step explanation:

$\sqrt{175} + \sqrt{112}$

5| 175

______

5| 35

______

****7

2| 112

______

2| 56

______

2| 28

______

2| 14

______

***7

$= \sqrt{5\times 5\times 7} + \sqrt{ 2\times 2\times 2\times 2\times 7}\\= 5\sqrt{7} + 4\sqrt{7}\\= 9\sqrt{7}$

Therefore.,

$\red { \sqrt{175} + \sqrt{112}}\green {=9\sqrt{7}}$

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Answer 2

$\sqrt{175} + \sqrt{112} \\ \\ = \sqrt{5 \times 5 \times 7} + \sqrt{2 \times 2 \times 2 \times 2 \times 7} \\ \\ = \sqrt{25 \times 7} + \sqrt{4 \times 4 \times 7} \\ \\ = 5 \sqrt{7} + 2 \sqrt{4 \times 7} \\ \\ = 5 \sqrt{7} + 2 \times 2 \sqrt{7} \\ \\ = 5 \sqrt{7} + 4 \sqrt{7} \\ \\ =( 5 + 4 )\sqrt{7} \\ \\ = \green{\boxed{9 \sqrt{7}}}$