Simplify the expression by rationalizing the denominator.?

Question

√10/7

Answer 1

I presume that you mean

sqrt(10/7)

When taking the square roots of fractions, we can express this as a fraction of square roots. That is

sqrt(10/7) = sqrt(10) / sqrt(7)

Mathematical etiquette doesn't want us to EVER have radicals in the denominator, hence why we need to rationalize the denominator.

Our first step would be to multiply the top and bottom by sqrt(7). Keep in mind that sqrt(7) times sqrt(7) would be 7.

[sqrt(10)sqrt(7)] / 7

Now the denominator is rationalized. However, we still have some simplification to do. The multiplication of any two square roots is the product of their insides.

sqrt(70)/7

Answer 2

Rationalize The Denominator And Simplify

Answer 3

The denominator already looks rationalized. But without parentheses the expression is ambigous. I assume you mean

√(10/7)

In that case

Multiply both numerator and denominator by √7.

√(10/7) = √(10*7/7²) = (√70)/7

In the future, use parentheses properly to avoid ambiguity. Improper lack of use of parenthesis is rampant on Yahoo Answers and we are constantly being left to guess what was probably meant. You risk a wrong answer due to a misunderstanding if a question is ambiguous.

Answer 4

If the expression is √(10/7) we have:

for rationalice, we multiply it by the same number up and dow in the fractio, so we can cancel the root in the denominator:

√(10/7) = √10 = √10*√7= √70
...............√7......√7*√7 ..... 7

like 70 can´t be factorized that we express it as a square root
tis is the final expression.

Answer 5

I can't tell by the way you have it written out,k but if your problem has the whole fraction under the radical sign (the square root sign), then you have to multiply both the top and the bottom of the fraction by the square root of 7.

This will give you a rational number on the bottom (which is what you want to do, it's the requirement (rationalize the denominator).

if you multiply both the top and bottom of the fraction by the square root of 7, then on the top you'll have the square root of 70, aand on the bottom you'll have 7.

Unless you can simplify the numerator (the top) by pulling a perfect square out of 70, then you have your final answer.

on the top you have the square root of 70 and on the bottom you have 7 (no square root sign).

Now you have moved the denominator (the bottom number) out from under the radical sign (the square root sign), but the top is still under it.

got it?

good luck and God bless you.

Answer 6

First: take the numerator and multiply it by the top and bottom:

[(V`10)(V`10)] / (V`10)(7)

V`100 / 7 V`10

Second: find the square root of 100 which is 10

10/7 V`10

Answer 7

√10/7=√10 * √1/7=√10*√7 /7=√70 / 7

Answer 8

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Answer 9

rt10*rt7/rt7*rt7
=rt70/7