root 45 simplified
Understand the Problem
The question is asking for the simplified form of the square root of 45. To solve this, we will factor 45 into its prime factors and simplify the square root accordingly.
Answer
$3\sqrt{5}$
Answer for screen readers
The simplified form of the square root of 45 is $3\sqrt{5}$
Steps to Solve
- Factor 45 into its prime factors
The prime factors of 45 are 3, 3, and 5. So, we can write:
$$45 = 3^2 imes 5$$
- Rewrite the square root using prime factors
We can use the property of square roots that states $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ to rewrite the expression:
$$\sqrt{45} = \sqrt{3^2 \times 5}$$
- Simplify the square root by taking the square root of the perfect square
The square root of $3^2$ is 3, so we can simplify:
$$\sqrt{3^2 \times 5} = 3 \times \sqrt{5}$$
Thus, the simplified form of $\sqrt{45}$ is $3 \sqrt{5}$.
The simplified form of the square root of 45 is $3\sqrt{5}$
More Information
Square roots are often simplified by factoring the number inside the square root into its prime factors and extracting the square root of any perfect squares.
Tips
A common mistake is forgetting to factor the number completely into its prime factors, which can result in an incorrect simplification.
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