Divide and Rationalize

[Mac_dw]

I seem to be having some difficulty with the following types of problems. I missed these three on an earlier exam, and I have a final comming up soon.

Prob 1) Square Root of 3/15

sqrt 1/5

= 1 / sqrt 5 (1 over sqrt of 5)

is this right now?
-------------------------------------------------

2) sqrt x^4/5

sqrt x^4 / sqrt 5

=x^2 / sqrt 5

Is my final answer x to the second power over the square root of 5?
If not where did I go wrong?
------------------------------------------------

3) sqrt 18yz / 75x^4y^5z^3

sqrt 18yz = (sqrt9)(sqrt2)(yz) = 3sqrt2yz

sqrt75x^4y^5z^3 = (sqrt25)(sqrt3)(x^4y^5z^3) = 5sqrt3x^4y^5z^3

3sqrt2yz / 5sqrt3x^4y^5z^3 = 3sqrt2 / 5sqrt3x^4y^4z^2

= 3sqrt2 / 5x^2y^2zsqrt3

How bout this one???

 

[stapel]

Your formatting is ambiguous.

1) \(\displaystyle \frac{\sqrt{3}}{15}?\,\,\sqrt{\frac{3}{15}}?\)

2) \(\displaystyle \frac{\sqrt{x}^4}{5}?\,\,\sqrt{x^{\frac{4}{5}}}?\,\,\sqrt{\frac{x^4}{5}}?\)

3) There are too many options on this one for me to guess.

Please reply using grouping symbols or some other form of clarification. Thank you.

Eliz.

 

[Mac_dw]

I would be glad to use grouping symbols unfortunately I am new to this???

I'm not clear on how to make this any more clear??? All 3 problems the entire irrational expression is the radicand???

your second guess on prob 1 is right

your 3rd guess on prob 2 is right

and it follows suit on prob 3

the square root of the entire expression 18yz/75(x to the fourth power)(y to the fifth power)(z to the third power)

Does that help??? any advice would be appreciated

 

[stapel]

All 3 problems the entire irrational expression is the radicand

So the exercises are as follows?

1) Simplify sqrt[3/15]

2) Simplify sqrt[ x⁴ / 5 ]

3) Simplify sqrt[ (18yz) / (75x⁴y⁵z³) ]

If so, then:

1) Multiply top and bottom by sqrt[5]. Simplify.

2) Same as for (1).

3) Simplify inside first, to get sqrt[ 6 / (25x⁴y⁴z² ]. Then take the square root.

Eliz.

 

[Mac_dw]

Yes you have the problems correct. Thank you for showing me how to express it better!!!

so Simplify sqrt[ x4 / 5 ] = (xsquared)(sqrt5) / 5

Simplify sqrt[3/15] = (sqrt5) / 5

Simplify sqrt[ (18yz) / (75x4y5z3) ] = (sqrt6) / (5)(x squared)(ysquared)(z)


Thank you!!! That makes sense. Now I remeber that we do not want a square root in the denominator and to do that multiply the denominator and the numerator by the denominators value.
sqrt[A/X] = sqrtA / sqrtX times sqrtX / sqrt X

 

[stapel]

...we do not want a square root in the denominator....

You don't want radicals in the denominators now, in algebra. You may be surprised, once you get to calculus, by how much they don't care any more. :wink:

Eliz.

 

[Denis]

I'm not clear on how to make this any more clear???
the square root of the entire expression 18yz/75(x to the fourth power)(y to the fifth power)(z to the third power)

Next time, go this way:

sqrt[18yz / (x^4 y^5 x^3)]

 

[Mac_dw]

Thanx Dennis!