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Square root problem!!!

Expert replies
Source: — Problem Solving |

by Anurag@Gurome » Mon Aug 08, 2011 9:45 am
jayanti wrote:√[2√63 + 2/(8+3√7)]

A. 8 + 3√7
B. 4 + 3√7
C. 8
D. 4
E. √7
2/(8 + 3√7) = 2*(8 - 3√7)/[(8 + 3√7)*(8 - 3√7)] = 2*(8 - 3√7)/[8² - (3√7)²] = 2*(8 - 3√7)/[64 - 63] = 2*(8 - 3√7) = 2*(8 - √63)

Hence, √[2√63 + 2/(8+3√7)] = √[2√63 + 2*(8 - √63)] = √[2√63 + 16 - 2√63)] = √16 = 4

The correct answer is D.
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by oex85 » Mon Aug 08, 2011 10:09 am
Anurag@Gurome wrote:
jayanti wrote:√[2√63 + 2/(8+3√7)]

A. 8 + 3√7
B. 4 + 3√7
C. 8
D. 4
E. √7
2/(8 + 3√7) = 2*(8 - 3√7)/[(8 + 3√7)*(8 - 3√7)] = 2*(8 - 3√7)/[8² - (3√7)²] = 2*(8 - 3√7)/[64 - 63] = 2*(8 - 3√7) = 2*(8 - √63)

Hence, √[2√63 + 2/(8+3√7)] = √[2√63 + 2*(8 - √63)] = √[2√63 + 16 - 2√63)] = √16 = 4

The correct answer is D.

Would just like an explanation for this part: 2*(8 - 3√7) = 2*(8 - √63)

How does 3√7 become √63? Clearly I need to hone my radical expression skills, but if you don't mind...

Also, what are the pros and cons for breaking down 2√63 into 2√7x3x3=5√7 ? Is it just by choice or is there some magical way to know...?

Thx.
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by Anurag@Gurome » Mon Aug 08, 2011 10:58 am
oex85 wrote:Would just like an explanation for this part: 2*(8 - 3√7) = 2*(8 - √63)
3 is equivalent to √9.
Hence, 3√7 = 3*(√7) = (√9)*(√7) = √(9*7) = √63
Thus, 2*(8 - 3√7) = 2*(8 - √63)
oex85 wrote:Also, what are the pros and cons for breaking down 2√63 into 2√7x3x3=5√7 ? Is it just by choice or is there some magical way to know...?
2√63 = 2√(7*3*3) = (2*3)√7 = 6√7

We can utilize this also in the same manner.
As mentioned earlier, 2/(8 + 3√7) = 2*(8 - 3√7) = (16 - 6√7)

Hence, √[2√63 + 2/(8+3√7)] = √[6√7 + 16 - 6√7] = √16 = 4
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by jayanti » Mon Aug 08, 2011 11:33 am
Thanks a lot Anurag Sir...... really helpful
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by oex85 » Mon Aug 08, 2011 12:43 pm
Thank you, Anurag.
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