Guide :

Simplify, radical 81x to the forth power.

## Research, Knowledge and Information :

### Simplify Radical Expressions - AlgebraLAB

Simplifying Radical Expressions: ... Simplifying a radical expression can also involve variables as well as numbers. ... Simplify #2. Simplify

### Algebra Examples | Radical Expressions and Equations ...

Radical Expressions and Equations. Simplify. Rewrite as . Pull terms out from under the radical, assuming positive real numbers.

### 6 Ways to Simplify Radical Expressions - wikiHow

Simplify any radical expressions that are perfect squares. A perfect square is the product of any number that is multiplied by itself, such as 81, which is the ...

Algebra 1 Radical expressions: The graph of a radical function Algebra 1 Radical expressions: The Pythagorean Theorem Algebra 1 Radical expressions: The distance and ...

### Simplifying radical expressions - free math help

Math lesson for simplifying radical expressions with examples, solutions and exercises.

The following calculator can be used to simplify ANY radical expression. To use it, replace radical sign with letter r . ... Simplifying Radical Expressions Calculator.

### Radicals: Introduction & Simplification | Purplemath

Introduces the radical symbol and the concept of taking roots. Covers basic terminology and demonstrates how to simplify terms containing square roots.

### Simplifying radical expressions: two variables | Algebra ...

A worked example of simplifying elaborate expressions that contain radicals with two variables. In this example, we simplify √(60x²y)/√(48x).

## Suggested Questions And Answer :

### sqrt(3a+10) = sqrt(2a-1) + 2

sqrt(3a+10)=sqrt(2a-1)+2 To remove the radical on the left-hand side of the equation, square both sides of the equation. (~(3a+10))^(2)=(~(2a-1)+2)^(2) Simplify the left-hand side of the equation. 3a+10=(~(2a-1)+2)^(2) Squaring an expression is the same as multiplying the expression by itself 2 times. 3a+10=(~(2a-1)+2)(~(2a-1)+2) Multiply each term in the first group by each term in the second group using the FOIL method. FOIL stands for First Outer Inner Last, and is a method of multiplying two binomials.  First, multiply the first two terms in each binomial group.  Next, multiply the outer terms in each group, followed by the inner terms.  Finally, multiply the last two terms in each group. 3a+10=(~(2a-1)*~(2a-1)+~(2a-1)*2+2*~(2a-1)+2*2) Simplify the FOIL expression by multiplying and combining all like terms. 3a+10=(~(2a-1)^(2)+4~(2a-1)+4) Remove the parentheses around the expression ~(2a-1)^(2)+4~(2a-1)+4. 3a+10=~(2a-1)^(2)+4~(2a-1)+4 Raising a square root to the square power results in the expression inside the root. 3a+10=(2a-1)+4~(2a-1)+4 Add 4 to -1 to get 3. 3a+10=2a+3+4~(2a-1) Since a is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation. 2a+3+4~(2a-1)=3a+10 Move all terms not containing ~(2a-1) to the right-hand side of the equation. 4~(2a-1)=-2a-3+3a+10 Simplify the right-hand side of the equation. 4~(2a-1)=a+7 Divide each term in the equation by 4. (4~(2a-1))/(4)=(a)/(4)+(7)/(4) Simplify the left-hand side of the equation by canceling the common terms. ~(2a-1)=(a)/(4)+(7)/(4) To remove the radical on the left-hand side of the equation, square both sides of the equation. (~(2a-1))^(2)=((a)/(4)+(7)/(4))^(2) Simplify the left-hand side of the equation. 2a-1=((a)/(4)+(7)/(4))^(2) Combine the numerators of all expressions that have common denominators. 2a-1=((a+7)/(4))^(2) Expand the exponent of 2 to the inside factor (a+7). 2a-1=((a+7)^(2))/((4)^(2)) Expand the exponent 2 to 4. 2a-1=((a+7)^(2))/(4^(2)) Simplify the exponents of 4^(2). 2a-1=((a+7)^(2))/(16) Multiply each term in the equation by 16. 2a*16-1*16=((a+7)^(2))/(16)*16 Simplify the left-hand side of the equation by multiplying out all the terms. 32a-16=((a+7)^(2))/(16)*16 Simplify the right-hand side of the equation by simplifying each term. 32a-16=(a+7)^(2) Since (a+7)^(2) contains the variable to solve for, move it to the left-hand side of the equation by subtracting (a+7)^(2) from both sides. 32a-16-(a+7)^(2)=0 Squaring an expression is the same as multiplying the expression by itself 2 times. 32a-16-((a+7)(a+7))=0 Multiply -1 by each term inside the parentheses. 32a-16-a^(2)-14a-49=0 Since 32a and -14a are like terms, add -14a to 32a to get 18a. 18a-16-a^(2)-49=0 Subtract 49 from -16 to get -65. 18a-65-a^(2)=0 Move all terms not containing a to the right-hand side of the equation. -a^(2)+18a-65=0 Multiply each term in the equation by -1. a^(2)-18a+65=0 For a polynomial of the form x^(2)+bx+c, find two factors of c (65) that add up to b (-18).  In this problem -5*-13=65 and -5-13=-18, so insert -5 as the right hand term of one factor and -13 as the right-hand term of the other factor. (a-5)(a-13)=0 Set each of the factors of the left-hand side of the equation equal to 0. a-5=0_a-13=0 Since -5 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 5 to both sides. a=5_a-13=0 Set each of the factors of the left-hand side of the equation equal to 0. a=5_a-13=0 Since -13 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 13 to both sides. a=5_a=13 The complete solution is the set of the individual solutions. a=5,13

### simplify the radical expression √600+5÷2√3-√6 ?

(sqrt(600)) + (5/(sqrt(3)) - sqrt(6) 10sqrt(6) + 5sqrt(1/3) - sqrt(6) 9sqrt(6) + 5sqrt(1/3)

### (5^4)^1/2 simplify the radical expression

(5^4)^1/2=5^2=25 ................

### (x+6)^2=28

Problem: (x+6)^2=28 usesquare root property,simplify radicals o rrationalize denominators express in for a+bi (x + 6)^2 = 28 x + 6 = √(28) x + 6 = ± 5.2915 x = ± 5.2915 - 6 x =  -0.7085   and   x = -11.2915

(√8)(√2)=4

(√x^3)(√x)=x^2

### In a paragraph, describe how to simplify each expression:

A rational exponent is another way of expressing a radical. For example, the exponent 1/3 is equivalent to a cube root. The exponent 1/2 is equivalent to a square root. So 16^1/2 is equal to the square root of 16 which is 4.

(√3)(√3)=3

(√x)(√x)=x