What is (sqrt(21)-sqrt(6))/(sqrt(35)-\sqrt{10)} ?

The solution to (sqrt(21)-sqrt(6))/(sqrt(35)-\sqrt{10)} is (sqrt(3))/(sqrt(5))

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simplify (sqrt(21)-sqrt(6))/(sqrt(35)-\sqrt{10)}

simplify

\frac{21 - 6}{35 - 10}

\frac{3}{5}

Decimal

0.77459 \dots

Solution steps

\frac{21 - 6}{35 - 10}

Multiply by the conjugate

\frac{35 + 10}{35 + 10}

= \frac{( 21 - 6 ) ( 35 + 10 )}{( 35 - 10 ) ( 35 + 10 )}

Expand

(21 - 6) (35 + 10) : 515

Expand

(35 - 10) (35 + 10) : 25

= \frac{5 15}{25}

Factor the number:

25 = 5 \cdot 5

= \frac{5 15}{5 \cdot 5}

Cancel the common factor:

5

= \frac{15}{5}

Factor

15 : 53

= \frac{5 3}{5}

Apply radical rule:

a = a a

5 = 55

= \frac{5 3}{5 5}

Cancel the common factor:

5

= \frac{3}{5}

(2 t + 5 x) (2 t - 5 x)

\frac{8 + 50 - 32}{2}

(4 z - 6) (4 z + 6)

19

2 (x - 4 y) + 3 (2 x + 3 y)

What is (sqrt(21)-sqrt(6))/(sqrt(35)-\sqrt{10)} ?
The solution to (sqrt(21)-sqrt(6))/(sqrt(35)-\sqrt{10)} is (sqrt(3))/(sqrt(5))