Answered

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Simplify the expression:

[tex]\[
\sqrt{45}
\][/tex]

[tex]\[
\sqrt{45} = \square
\][/tex]

(Type an exact answer, using radicals as needed.)

Sagot :

GinnyAnswer
To simplify the expression [tex]\(\sqrt{45}\)[/tex]:

1. First, we identify the factors of 45:
[tex]\[ 45 = 9 \times 5 \][/tex]

2. Next, we use the property of square roots that states [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex]:
[tex]\[ \sqrt{45} = \sqrt{9 \times 5} \][/tex]

3. We know that 9 is a perfect square, and [tex]\(\sqrt{9} = 3\)[/tex]:
[tex]\[ \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} \][/tex]

4. Substituting the value of [tex]\(\sqrt{9}\)[/tex]:
[tex]\[ \sqrt{9} \times \sqrt{5} = 3 \times \sqrt{5} \][/tex]

Therefore, the simplified expression is:
[tex]\[ \sqrt{45} = 3 \times \sqrt{5} \][/tex]
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