Best answer:
One foolproof way to simplify square roots is to completely factor the number into its prime factorization:
For any number that appears twice, bring *one* copy outside the radical symbol. Leave the rest inside:
√18
= √(2 * 3 * 3)
= 3√2
Here's your example with √24:
√24
= √(2 * 2 * 2 * 3)
= 2√(2 * 3)
=...
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Best answer: One foolproof way to simplify square roots is to completely factor the number into its prime factorization:
For any number that appears twice, bring *one* copy outside the radical symbol. Leave the rest inside:
√18
= √(2 * 3 * 3)
= 3√2
Here's your example with √24:
√24
= √(2 * 2 * 2 * 3)
= 2√(2 * 3)
= 2√6
Let's try a harder example with √600:
√600
= √(2 * 2 * 2 * 3 * 5 * 5)
= (2 * 5)√(2 * 3)
= 10√6
But you don't always need to go down to the complete prime factorization. Try to look for factors that are perfect squares. For example, in 18, you know that 9 is a perfect square factor:
√18
= √9 * √2
= 3√2
In 24, you can see that 4 is a perfect square factor.
√24
= √4 * √6
= 2√6
So look for square factors like 4, 9, 16, 25, etc.
For example, 600 has 100 as a perfect square factor:
√600
= √100 * √6
= 10√6
10 answers
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2 days ago