Question about a square root concept?

[blitzburgh]

hello, I need no know how you would multiply a set of square roots such as: 3?5 x 3?5 (3 IS THE INDEX and x is a multiplication sign). Is it the same as 2?5 x 2?5 (3 IS THE INDEX and x is a multiplication sign) where the answer would just be 5? thanks

 

[tkhunny]

Why is it different, whether it be a cube root or a square root? Ponder the exponential equivalent and it should become clear.

\(\displaystyle \sqrt[3]{5}\;=\;5^{1/3}\)

With some restrictions that we can talk about later, just use regular rules of exponents.

 

[mmm4444bot]

square roots such as: 3?5 x 3?5 (3 IS THE INDEX and x is a multiplication sign).

Oops! These factors are not square roots; they are cube roots.

(If the index is not two, the radical is not a square root.)


Is it the same as 2?5 x 2?5 (2 IS THE INDEX and x is a multiplication sign) where the answer would just be 5?

No, it's not the same as with cube roots, and I corrected (in red) your typographical error above.

With cube roots, you need three factors multiplied together, in order for their product to equal the radicand (which is 5).

Therefore, the cube root of 5 multiplied by the cube root of 5 is NOT 5.

There is a property of radicals that tells us that the cube root of 5 times the cube root of 5 equals the cube root of 5^2. Have you seen properties of radicals, yet?

 

[JeffM]

hello, I need no know how you would multiply a set of square roots such as: 3?5 x 3?5 (3 IS THE INDEX and x is a multiplication sign). Is it the same as 2?5 x 2?5 (3 IS THE INDEX and x is a multiplication sign) where the answer would just be 5? thanks

This is an odd question to post on a board about intermediate algebra, but I am going to assume that you are studying beginning algebra. In general, if you post a question on the wrong board, you may not get all the information that you need.

Let's go back to basics. The radicand is what is inside the radical. You clearly know what the index is. The whole thing is called the __th root of the radicand, where you fill in the blank with the index. There are special names if the index is 2 or 3, namely square root and cube root, but the principal and notation can be extended to any whole number. OK, that is the vocabulary.

The square (or second) root of n is the number m such that (m X m) = n. (It's similar to computing the area of a square; hence the name.)

The cube (or third) root of n is the number q such that (q X q X q) = n. (It's similar to computing the volume of a perfect cube; hence the name.)

The fourth root of n is the number p such that (p X p X p X p) = n. So the fourth root of 16 is 2 because (2 X 2 X 2 X 2) = 16.

See the pattern.

Let's take an example. The square root of 64 is 8 because (8 times 8) = 64. The cube root of 64 is 4 because (4 times 4 times 4) = 64.
It is FALSE that (4 X 4) = (8 X 8).

It should now be obvious why multiplying the cube root of 5 by the cube root of 5 does not give you 5 whereas multiplying the square root of five by the square root of 5 does give you five. The cube root and the square root always have different definitions and almost always represent different numbers.

Now re-read the preceding replies.

 

[blitzburgh]

Why is it different, whether it be a cube root or a square root? Ponder the exponential equivalent and it should become clear.

\(\displaystyle \sqrt[3]{5}\;=\;5^{1/3}\)

With some restrictions that we can talk about later, just use regular rules of exponents.

thanks

 

[blitzburgh]

hello, I need no know how you would multiply a set of square roots such as: 3?5 x 3?5 (3 IS THE INDEX and x is a multiplication sign). Is it the same as 2?5 x 2?5 (3 IS THE INDEX and x is a multiplication sign) where the answer would just be 5? thanks

This is an odd question to post on a board about intermediate algebra, but I am going to assume that you are studying beginning algebra. In general, if you post a question on the wrong board, you may not get all the information that you need.

Let's go back to basics. The radicand is what is inside the radical. You clearly know what the index is. The whole thing is called the __th root of the radicand, where you fill in the blank with the index. There are special names if the index is 2 or 3, namely square root and cube root, but the principal and notation can be extended to any whole number. OK, that is the vocabulary.

The square (or second) root of n is the number m such that (m X m) = n. (It's similar to computing the area of a square; hence the name.)

The cube (or third) root of n is the number q such that (q X q X q) = n. (It's similar to computing the volume of a perfect cube; hence the name.)

The fourth root of n is the number p such that (p X p X p X p) = n. So the fourth root of 16 is 2 because (2 X 2 X 2 X 2) = 16.

See the pattern.

thanks man i got it now

Let's take an example. The square root of 64 is 8 because (8 times 8) = 64. The cube root of 64 is 4 because (4 times 4 times 4) = 64.
It is FALSE that (4 X 4) = (8 X 8).

It should now be obvious why multiplying the cube root of 5 by the cube root of 5 does not give you 5 whereas multiplying the square root of five by the square root of 5 does give you five. The cube root and the square root always have different definitions and almost always represent different numbers.

Now re-read the preceding replies.