Whats the anawer to ill send u a picture of the questions

Question

Simplify the square root of 75

 

Answer 1

To simplify √75, you first look for factors of 75, one of which is a perfect square (25 and 3).  Then, you take the square root of the perfect square and bring it out front of the radical sign, leaving the other number underneath the radical sign:

 

√75

√(25 * 3)

5√3

 

You can check that √75 equals 5√3 with a calculator to check your answer.

Answer 2

To simplify the square root of a number, choose factors of the number that are perfect squares.  The square roots of any perfect square factors will 'pop out' in front, e.g.  √(75) = √(3•25) = 5√3.

 

Another example: Square root of 24 should be considered as square root of 4(6) rather than square root of (2)(12) or square root of 3(8)--because 4 is the largest perfect square factor of 24.  Thus √(24) = √(4•6) = 2√6.

Answer 3

First, break 75 into its prime factors: 3, 5, 5.

Right now, you have 3 · 5 · 5 under the radical sign.

If you have a pair, you can simplify, by putting one of its members (a 5) in front of the radical sign, and removing the other one, since the square root of 5² is 5.

The 3 remains under the radical sign, because it is not paired, so √75 simplifies to 5√3.