What is the square root of 45?
Understand the Problem
The question is asking for the square root of the number 45. To solve it, we will determine the value that, when multiplied by itself, equals 45.
Answer
$3 \sqrt{5}$
Answer for screen readers
The final answer is $3 \sqrt{5}$
Steps to Solve
- Identify the problem with square root calculations
We need to find the value that, when multiplied by itself, equals 45.
$$ \sqrt{45} $$
- Simplify the square root
To simplify $\sqrt{45}$, factorize 45 into its prime factors:
$$ 45 = 3^2 \times 5 $$
- Apply the square root to the factors
Using the property of square roots, $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$:
$$ \sqrt{45} = \sqrt{3^2 \times 5} = \sqrt{3^2} \times \sqrt{5} $$
Since $\sqrt{3^2} = 3$:
$$ \sqrt{45} = 3 \times \sqrt{5} $$
- Provide the simplified form of the square root
The simplified form of the square root of 45 is $3 \sqrt{5}$.
The final answer is $3 \sqrt{5}$
More Information
Square roots can often be simplified by finding the prime factors and taking out pairs of factors to simplify the expression. This technique is useful for many non-perfect square numbers.
Tips
A common mistake is to forget to simplify the square root by not taking out the perfect squares from under the radical.
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