Question

Simplify 4 square root 6 over square root 30 by rationalizing the denominator.

Answer 1

To simplify the expression, we first simplify the numerator:

4√6 = 4 * √(2*3) = 4√2√3 = 4√2√3

Next, simplify the denominator:

√30 = √(2*15) = √2√15

Now rewrite the fraction in simplified form:

4√2√3 / √2√15

Rationalize the denominator by multiplying both the numerator and the denominator by √15:

(4√2√3 * √15) / (√2√15 * √15)

This simplifies to:

(4 * √30) / 15

The final simplified form is 4√30 / 15.

Answer 2

are you sure

Answer 3

I apologize for the mistake in my previous response. Let me correct it.

Given expression: 4√6 / √30

To simplify, we first simplify the numerator:

4√6 = 4 * √6 = 4 * √(2*3) = 4 * √2 * √3 = 4√2√3

Next, simplify the denominator:

√30 = √(2*15) = √2 * √15

Now rewrite the fraction in simplified form:

4√2√3 / √2√15

Rationalize the denominator by multiplying both the numerator and the denominator by √15:

(4√2√3 * √15) / (√2√15 * √15)

This simplifies to:

(4√90) / 15

Further simplifying:

4√90 = 4 * √(9 * 10) = 4 * 3 * √10 = 12√10

Therefore, the final simplified form is 12√10 / 15, which can be further reduced by dividing both the numerator and the denominator by 3 to get:

4√10 / 5