How do you simplify sqrt14/(3sqrt35)?

2 Answers
Tony B
Sep 6, 2016

sqrt10/15

Explanation:

Write as " "sqrt(2xx7)/(3sqrt(5xx7))

(sqrt(2)xx cancel(sqrt(7)))/(3xxsqrt(5)xx cancel(sqrt(7)))

sqrt(2)/(3sqrt(5))

If at all possible mathematicians like to 'get rid' of any roots in the denominator (bottom number).

Multiply by 1 but in the form 1=sqrt5/sqrt5

sqrt(2)/(3sqrt(5))xx1" " ->" "sqrt(2)/(3sqrt(5))xxsqrt5/sqrt5

but " "sqrt5xxsqrt5 =5

(sqrt2sqrt5)/(3xx5)

sqrt10/15

Tazwar Sikder
Sep 6, 2016

(sqrt(10)) / (15)

Explanation:

We have: (sqrt(14)) / (3 sqrt(35))

Let's express the radicals as products:

= (sqrt(2 cdot 7)) / (3 cdot sqrt(5 cdot 7))

= (sqrt(2) cdot sqrt(7)) / (3 cdot sqrt(5) cdot sqrt(7))

We can cancel the sqrt(7) terms:

= (sqrt(2)) / (3 sqrt(5))

Finally, let's rationalise the denominator:

= (sqrt(2)) / (3 sqrt(5)) cdot (sqrt(5)) / (sqrt(5))

= (sqrt(10)) / (3 cdot 5)

= (sqrt(10)) / (15)

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