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1. Simplify [tex]\sqrt[4]{32}[/tex].

Sagot :

GinnyAnswer
To simplify [tex]\(\sqrt[4]{32}\)[/tex], let's break it down step by step:

1. Express 32 as a power of 2:

[tex]\[ 32 = 2^5 \][/tex]

2. Rewrite the radical expression in terms of exponents:

[tex]\[ \sqrt[4]{32} = \sqrt[4]{2^5} \][/tex]

3. Apply the property of exponents:

Using the property [tex]\(\sqrt[n]{a^m} = a^{m/n}\)[/tex], we can rewrite the expression as:

[tex]\[ \sqrt[4]{2^5} = 2^{5/4} \][/tex]

4. Evaluate the exponent:

To find the value of [tex]\(2^{5/4}\)[/tex], we compute [tex]\(2\)[/tex] raised to the power of [tex]\(\frac{5}{4}\)[/tex].

[tex]\[ 2^{5/4} \approx 2.378414230005442 \][/tex]

Thus, the simplified form of [tex]\(\sqrt[4]{32}\)[/tex] is approximately [tex]\(2.378414230005442\)[/tex].
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