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# Square roots

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Simplify the expression 1/sqrt(2) + 3/sqrt(8) + 5/sqrt(32).

Jan 31, 2022

#1
+1209
+3

$$\frac{1}{\sqrt{2}} + \frac{3}{\sqrt{8}}+\frac{5}{\sqrt{32}}$$

$$= \frac{\sqrt{2}}{\sqrt{2}} \cdot \frac{1}{\sqrt{2}} + \frac{3}{2\sqrt{2}} + \frac{5}{4\sqrt{2}}$$

$$= \frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{\sqrt{2}} \cdot \frac{3}{2 \sqrt{2}} + \frac{\sqrt{2}}{\sqrt{2}} \cdot \frac{5}{4\sqrt{2}}$$

$$= \frac{\sqrt{2}}{2} + \frac{3 \sqrt{2}}{4} + \frac{5 \sqrt{2}}{8}$$

$$= \frac{4 \sqrt{2} + 6\sqrt{2} + 5\sqrt{2}}{8}$$

$$=\boxed{\frac{15\sqrt{2}}{8}}$$

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Jan 31, 2022
#2
+360
+3

$$\frac{1}{\sqrt{2}}+\frac{3}{\sqrt{8}}+\frac{5}{\sqrt{32}}$$

$$\frac{1}{\sqrt{2}}+\frac{3}{2\sqrt{2}}+\frac{5}{4\sqrt{2}}$$

$$\frac{4}{4\sqrt{2}}+\frac{6}{4\sqrt{2}}+\frac{5}{4\sqrt{2}}$$

$$\frac{15}{4\sqrt{2}}$$

Jan 31, 2022
#3
+1209
+2

These answers are equivalent, as shown below:

$$\frac{15}{4 \sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \boxed{\frac{15\sqrt{2}}{8}}$$

This process is called rationalizing the denominator.

CubeyThePenguin  Jan 31, 2022
#4
+360
+4

totally forgot alll about that lol

thanks you for reminding me!

Feb 2, 2022