How do you rationalize the denominator and simplify $\frac{\sqrt{21}}{\sqrt{35}}$ $sqrt21/sqrt35$ ?

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Answer 1 · 2017-09-06T07:38:18

$= \frac{\sqrt{15}}{5}$ $=sqrt15/5$

multiply top and bottom by $\sqrt{35}$ $sqrt35$

$\frac{\sqrt{21}}{\sqrt{35}} \times \frac{\sqrt{35}}{\sqrt{35}}$ $sqrt21/sqrt35xxsqrt35/sqrt35$

$= \frac{\sqrt{21} \sqrt{35}}{35}$ $=(sqrt21sqrt35)/35$

now combine the sqrt on the numerator and simplify as shown

$\frac{\sqrt{21 \times 35}}{35} = \frac{\sqrt{3 \times 7 \times 5 \times 7}}{35}$ $sqrt(21xx35)/35=sqrt(3xx7xx5xx7)/35$

$= \frac{\sqrt{7^{2} \times 15}}{35}$ $=(sqrt(7^2xx15))/35$

$=(cancel(7)sqrt15)/cancel(35)^5$

$=sqrt15/5$

Answer 2 · 2017-09-06T11:19:55

Slightly different approach demonstrating that you can 'split' roots

$sqrt(15)/5$

Given: $sqrt21/sqrt35$

Note that $5xx7=35 and 3xx7=21$

Write as: $(sqrt(3)xxcancel(sqrt(7)))/(sqrt(5)xxcancel(sqrt(7)))$

Giving $sqrt3/sqrt5$

Multiply by 1 and you do not change the value. However, 1 comes in many forms.

$color(green)(sqrt3/sqrt5color(red)(xx1) color(white)("ddd") ->color(white)("ddd")sqrt3/sqrt5color(red)(xxsqrt5/sqrt5)) = sqrt(15)/5$

How do you rationalize the denominator and simplify sqrt21/sqrt35√21√35sqrt21/sqrt35?