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

1)
`\mathbf{√(50)= 5√(2) }`

2)
`\mathbf{√(28)= 2√(7) }`

3)
`\mathbf{√(252)= 6√(7) }`

Explanation:

We need to simplify the radicals:

1)
`√(50)`

First we find prime factors of 50

50 = 2 x 5 x 5

Now,

`√(50)\\=√(2* 5* 5)\\=√(2* 5^2)\\ =√(2) √(5^2)\\=5√(2)`

So,
`\mathbf{√(50)= 5√(2) }`

2)
`√(28)`

First we find prime factors of 28

28 = 2 x 2 x 7

Now,

`√(28)\\=√(2* 2* 7)\\=√(2^2* 7)\\ =√(2^2) √(7)\\=2√(7)`

So,
`\mathbf{√(28)= 2√(7) }`

3)
`√(252)`

First we find prime factors of 252

50 = 2 x 2 x 3 x 3 x 7

Now,

`√(252)\\=√(2* 2* 3* 3 *7)\\=√(2^2* 3^2 *7)\\ =√(2^2) √(3^2)√(7) \\=2* 3√(7)\\=6√(7)`

So,
`\mathbf{√(252)= 6√(7) }`