Question

(2√15)+√5) : √5 -2√3

Answer 1

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Answer 2

To simplify the expression, let's break it down step by step:

(2√15 + √5) : (√5 - 2√3)

First, let's rationalize the denominator (√5 - 2√3):

Multiply the numerator and denominator by the conjugate of (√5 - 2√3), which is (√5 + 2√3):

((2√15 + √5) * (√5 + 2√3)) / ((√5 - 2√3) * (√5 + 2√3))

Expanding the numerator and the denominator:

(2√15 * √5 + 2√15 * 2√3 + √5 * √5 + √5 * 2√3) / (√5 * √5 - 2√3 * √5 + √5 * 2√3 - 2√3 * 2√3)

Simplifying further:

(2√75 + 4√45 + 5 + 2√15) / (5 - 2√15 + 2√15 - 12)

Combining like terms:

(2√75 + 4√45 + 5 + 2√15) / (-7)

Next, divide each term by -7:

2/(-7) * √75 + 4/(-7) * √45 + 5/(-7) + 2/(-7) * √15

Simplifying the fractions:

-2/7 * √75 - 4/7 * √45 - 5/7 - 2/7 * √15

Finally, rearranging the terms:

• (2/7)√75 - (4/7)√45 - (5/7) - (2/7)√15

This is the simplified form of the expression.