Math Problem Statement

Fully simplify √90

Solution

To fully simplify 90\sqrt{90}, we need to find the prime factorization of 90.

First, express 90 as a product of prime factors: 90=2×32×590 = 2 \times 3^2 \times 5

Now, break the square root into parts: 90=2×32×5\sqrt{90} = \sqrt{2 \times 3^2 \times 5}

Since 323^2 is a perfect square, we can take 3 out of the square root: 90=32×5=310\sqrt{90} = 3\sqrt{2 \times 5} = 3\sqrt{10}

Thus, the fully simplified form of 90\sqrt{90} is: 310\boxed{3\sqrt{10}}

Would you like further details, or do you have any questions?

Here are 5 related questions:

  1. How would you simplify 72\sqrt{72}?
  2. Can you express 45\sqrt{45} in its simplest form?
  3. How can prime factorization help simplify square roots?
  4. What happens if you try to simplify 200\sqrt{200}?
  5. What is the simplest form of 50\sqrt{50}?

Tip: Always look for perfect square factors when simplifying square roots.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Simplification of square roots
Prime factorization

Formulas

√a × b = √a × √b
Prime factorization

Theorems

Properties of square roots

Suitable Grade Level

Grades 7-9