square root?

Question

how can you write a square root of a number for instance what is the equivalent of the square root of 2 without writing it with a radical

so if I wanted to rewrite square root of 8 just raise it to 1/2?

Answer 1

You could write it as an exponent.

Like in your example with the square root of 2.
Just raise 2 to the (1/2) power.
Like this: 2^(1/2)

Answer 2

If you don't want to use the radical, you can write something like "1.41421", which is the _approximate_ value of the square root of 2. The problem is, with most square roots, you cannot express their values exactly in digits. For example, the digits in the square root of 2 go on forever, with no repeating pattern!

For this reason, if you're using sqrt(2) in an algebra problem (in real life as well as in the classroom), you normally would not want to eliminate the radical while you're manipulating the equation. That's because if you switch from the "exact" form ("sqrt(2)") to the "approximate" form ("1.41421"), you actually can sometimes mess up the equation you were trying to solve.

So what people usually do is: keep the radical in the equation until the equation is completely solved; and THEN, at the very end, they'll actually substitute the (approximate) digits so they can have a final answer that looks like a real number.

Now, if your question is, "how do you calculate square roots?" (and assuming you don't want to just use a calculator); that's almost a lost art. They used to teach that in school when I was a kid (in the 1960's); but that was because there were no calculators back then. They rarely teach it today. Here's a website that can show you some ways: http://www.homeschoolmath.net/teaching/square-root-algorithm.php

Answer 3

Even though it is not always written out, the radical usually has a little number written "on top of the house". A square root is symbolized by a radical that has a 2 "on top of the house".

WIth that in mind: The x-root (aka the number "on top of the house") of a number y raised to the power z is the same as y^(z/x).


The square root of any number (x) raised to any power (y) is the same as that number (x) raised to the "y divided by 2" power.

Example: sqrt(2) = sqrt(2^1).
This is 2 to the power of 1, under a radical that has a 2 "on top of the house".
sqrt(2^1) = 2^(1/2).
Answer: This is 2 raised to the power of 1/2.

Another example, using cube root:
Example: cubert(27) = cubert(27^1).
This is 27 to the power of 1, under a radical that has a 3 "on top of the house"
cubert(27^1) = 27^(1/3)
This is 27 raised to the power of 1/3.

To see a clear picture of the above, look at the first sentence of the "Cube root" link from the source list below.

Answer 4

The radical sign is just a shorthand for the 1/2 power.
Radical 2 can be written 2^(1/2).
Note also that the square root may be positive or negative while the radical is the positive square root.

Answer 5

The square root also equals the power of 0.5. So anything with a square root is also to the power of 1/2. So the square root of 2 is 2^0.5 or 2^(1/2)

Answer 6

the square root of 2 is about 1.4.

1.4 times 1.4 is 1.96

Answer 7

2^.5

Answer 8

sqrt(2)=1.4142. answer