Question

Rewrite each of the following expressions so that the number inside the radical is as small as possible. For example, rewrite √18 as 3√2.
√50= 

√28= 

√252=

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Answer 1

Answer:

1)  $\mathbf{\sqrt{50}= 5\sqrt{2} }$

2) $\mathbf{\sqrt{28}= 2\sqrt{7} }$

3) $\mathbf{\sqrt{252}= 6\sqrt{7} }$

Step-by-step explanation:

We need to simplify the radicals:

1) $\sqrt{50}$

First we find prime factors of 50

50 = 2 x 5 x 5

Now,

$\sqrt{50}\\=\sqrt{2\times 5\times 5}\\=\sqrt{2\times 5^2}\\ =\sqrt{2} \sqrt{5^2}\\=5\sqrt{2}$

So, $\mathbf{\sqrt{50}= 5\sqrt{2} }$

2) $\sqrt{28}$

First we find prime factors of 28

28 = 2 x 2 x 7

Now,

$\sqrt{28}\\=\sqrt{2\times 2\times 7}\\=\sqrt{2^2\times 7}\\ =\sqrt{2^2} \sqrt{7}\\=2\sqrt{7}$

So, $\mathbf{\sqrt{28}= 2\sqrt{7} }$

3) $\sqrt{252}$

First we find prime factors of 252

50 = 2 x 2 x 3 x 3 x 7

Now,

$\sqrt{252}\\=\sqrt{2\times 2\times 3\times 3 \times7}\\=\sqrt{2^2\times 3^2 \times7}\\ =\sqrt{2^2} \sqrt{3^2}\sqrt{7} \\=2\times 3\sqrt{7}\\=6\sqrt{7}$

So, $\mathbf{\sqrt{252}= 6\sqrt{7} }$