$\sqrt{44100}$

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Warm-up:

Prime Factor Decomposition
(care of revisionworld.com)

The Problem:

What is $\sqrt{44100}$ ?

Given that $4410 = 2 \times 3^{2} \times 5 \times 7^{2}$ .

Tip: you don't need a calculator.

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Solution:

This is a problem about factors and noticing that

44100 = 4410 \times 10

44100 = 2 \times 3^{2} \times 5 \times 7^{2} \times 2 \times 5

44100 = 2^{2} \times 3^{2} \times 5^{2} \times 7^{2}

So ...

\sqrt{44100} = \sqrt{2^{2} \times 3^{2} \times 5^{2} \times 7^{2}}

\sqrt{44100} = 2 \times 3 \times 5 \times 7

\sqrt{44100} = 210

Further Reading:

Prime Factors
(care of www.savemyexams.co.uk)

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Don't Panic! Quadratics and Circle Theorems

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