Question

Simplify the radical expression. $$\sqrt{9900}$$

Short answer

Therefore, the simplified form of \( \sqrt{9900} \) is 2 * 5 * 11 = 110.

Step-by-step solution

Prime factorize the number

To simplify a radical, begin by prime factorizing the number under the root. In this case, prime factorize 9900. This can be done by finding numbers that multiply together to give 9900 and that cannot be further subdivided. Here, it factorizes to \(2^2 * 3^1 * 5^2 * 11^2\).

Identify and take out pairs

A pair of factors can be removed from under the radical by taking one of the numbers of the pair out. So, identify all pairs in the prime factorisation. Here 2,5 and 11 are the pairs of factors, each appearing twice (a pair).

Pull out the pairs

Pull out the pairs. So, take the numbers 2, 5 and 11 out of the root, which leaves nothing under the root since there are no remaining factors. This simplification is possible since the square root of a pair of identical factors equals just one of those factors.