Boone Weaver
05/19/2024 · Middle School
\( \sqrt{a^{2}+12 a b+36 b^{2}} \) при \( a=7 \frac{2}{5}, b=\frac{3}{5} \);
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Substitute \( a=7.4,b=0.6 \) into the expression \( \sqrt{a^{2}+12ab+36b^{2}} \).
Evaluate the expression by following steps:
- step0: Evaluate:
\(\sqrt{a^{2}+12ab+36b^{2}}\)
- step1: Substitute:
\(\sqrt{7.4^{2}+12\times 7.4\times 0.6+36\times 0.6^{2}}\)
- step2: Convert the expressions:
\(\sqrt{\left(\frac{37}{5}\right)^{2}+12\times 7.4\times 0.6+36\times 0.6^{2}}\)
- step3: Convert the expressions:
\(\sqrt{\left(\frac{37}{5}\right)^{2}+12\times 7.4\times 0.6+36\left(\frac{3}{5}\right)^{2}}\)
- step4: Multiply the terms:
\(\sqrt{\left(\frac{37}{5}\right)^{2}+53.28+36\left(\frac{3}{5}\right)^{2}}\)
- step5: Multiply the terms:
\(\sqrt{\left(\frac{37}{5}\right)^{2}+53.28+\frac{324}{25}}\)
- step6: Add the numbers:
\(\sqrt{121}\)
- step7: Write in exponential form:
\(\sqrt{11^{2}}\)
- step8: Simplify the root:
\(11\)
При \( a=7.4 \) и \( b=0.6 \) выражение \( \sqrt{a^{2}+12ab+36b^{2}} \) равно 11.
Quick Answer
При \( a=7.4 \) и \( b=0.6 \) выражение \( \sqrt{a^{2}+12ab+36b^{2}} \) равно 11.
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