Algebraic Simplifying?

Question

Could someone please either solve these or tell me how to do it.

*Simplify the following*

- SQRT363 X^6 Y^3

SQRT15 + SQRT60 - SQRT135

3^SQRT64

SQRT2 over SQRT3 XY

(3 SQRT2 + 2 SQRT5) (4 SQRT2 -SQRT5)

SQRT-3 + SQRT -27

2 SQRT-6 (SQRT-2 + 4 SQRT-6)

SQRT -2 over SQRT 9

6 over 4 + 3i

Thank You very much to anyone who answers! :)

Answer 1

I can hopefully show you how and you can apply rules for others:

6 over 4 + 3i: multiply by (4 - 3i)/(4 - 3i) to get rid of imaginary number in denominator (rule). You get (24 - 18i)/(16 -9i squared)

This simplifies to (24-18i)/(25) .....9i squared: i squared= -1


SQRT15 + SQRT60 - SQRT135= (SQRT 3 * SQRT 5) + (SQRT 3 * SQRT 5 * SQRT 4) - (SQRT 9 * SQRT 9 * SQRT 5)

factor SQRT 5....take SQRT of 4 and 9s....

SQRT 5(SQRT 3 + 2*SQRT3 - 9)

3^SQRT64.....calculate SQRT64; raise 3 by that number, ie 3EXP8 (don't have my calculator)

Rules:

1. roots multiply....multiple coefficients and then multiply number under root (3 SQRT2 + 2 SQRT5) (4 SQRT2 -SQRT5) first term = 12 SQRT 4, etc.

2. Cannot have root in denominator

3. roots add if they have common number under SQRT symbol, ie 3*SQRT 2 + 5*SQRT 2 = 8*SQRT 2

Hope this helps!

Answer 2

The first expression isn't clear to me.

sqrt15+sqrt60-sqrt135= sqrt15+sqrt(4*15)-sqrt(9*15)
=sqrt15+2*sqrt15-3*sqrt15=0

3^sqrt64= 3^ 8= 6561

(3sqrt2+2sqrt5) (4sqrt2-sqrt5)=3sqrt2(4sqrt2-sqrt5)+2sqrt5(4sqrt2-sqrt5)= 24-3sqrt10-10+8sqrt10= 14+5sqrt10

sqrt-3+sqrt-27= (sqrt3)i+(sqrt27)i= (sqrt3+3sqrt3)i=(4sqrt3)i

Answer 3

a million. first use the distributive belongings to get 4*5y - 4*3 -2*6y +(-2)*3 then do multiplications to get 20y - 12 -12y - 6 then upload like words to get 8y -18 2. in case you have the comparable base selection, on your question it relatively is a 5, then you definately subtract the exponent interior the denominator from the only interior the numerator so the question will become 5^(3-5) which simplifies to 5^-2 that would additionally be written as a million/5^2 or a million/25