Question

1 Simplify the following √18×√20×√24/√8×√30 Ans​

Answer 1

√6.

Explanation:

To simplify the expression, you can combine the square roots:

√18 × √20 × √24 / √8 × √30

First, factor the numbers under the square roots to identify perfect squares:

√(2 × 3 × 3) × √(2 × 2 × 5) × √(2 × 2 × 2 × 3) / √(2 × 2 × 2) × √(2 × 3 × 5)

Now, you can simplify by canceling out common factors inside the square roots:

√(3) × √(2 × 5) × √(2 × 3) / √(2) × √(3 × 5)

Next, simplify further by multiplying the numbers outside the square roots:

√(3) × √(10) × √(6) / √(2) × √(15)

Now, you can combine the square roots:

√(3 × 10 × 6) / √(2 × 15)

Simplify the numbers under the square roots:

√(180) / √(30)

Since both the numerator and denominator have the same square root, you can simplify further:

√(180 / 30)

Now, simplify the fraction:

√(6)

So, the simplified answer is √6.