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# Square root question ?

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what is the exact square root of 37.6765?

happygal  Aug 24, 2017
#1
+2139
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$$\sqrt{37.6765}\approx 6.1381186042630359$$

Unfortunately, I cannot give you all the decimal places for this answer as it is irrational; any radicand that is not a perfect square yields an irrational result.

TheXSquaredFactor  Aug 24, 2017
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happygal wants the exact answer, not a decimal answer.  If you look at my answer, you will see an exact answer in fraction form.

gibsonj338  Aug 24, 2017
#4
+2139
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Ok, I understand. I'll leave the answer up just in case this user needs the decimal approximation.

TheXSquaredFactor  Aug 24, 2017
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+1841
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$$\sqrt{37.6765}$$

$$\sqrt{37\frac{6765}{10000}}$$

$$\sqrt{\frac{376765}{10000}}$$

$$\sqrt{\frac{75353}{2000}}$$

$$\frac{\sqrt{75353}}{\sqrt{2000}}$$

$$\frac{\sqrt{75353}}{\sqrt{400}\sqrt{5}}$$

$$\frac{\sqrt{75353}}{20\sqrt{5}}$$

$$\frac{\sqrt{75353}}{20\sqrt{5}}\times\frac{\sqrt{5}}{\sqrt{5}}$$

$$\frac{\sqrt{75353}\sqrt{5}}{20\sqrt{5}\sqrt{5}}$$

$$\frac{\sqrt{376765}}{20\sqrt{5}\sqrt{5}}$$

$$\frac{\sqrt{376765}}{20\sqrt{25}}$$

$$\frac{\sqrt{376765}}{20\times5}$$

$$\frac{\sqrt{376765}}{100}$$

gibsonj338  Aug 24, 2017