Question
Simplify the expression
900z2−10
Evaluate
(3z×10)2−10
Multiply the terms
(30z)2−10
Solution
900z2−10
Show Solution

Factor the expression
10(90z2−1)
Evaluate
(3z×10)2−10
Multiply the terms
(30z)2−10
Simplify
More Steps

Evaluate
(30z)2
Rewrite the expression
30z×30z
Multiply the numbers
900z×z
Multiply the terms
900z2
900z2−10
Solution
10(90z2−1)
Show Solution

Find the roots
z1=−3010,z2=3010
Alternative Form
z1≈−0.105409,z2≈0.105409
Evaluate
(3z×10)2−10
To find the roots of the expression,set the expression equal to 0
(3z×10)2−10=0
Multiply the terms
(30z)2−10=0
Rewrite the expression
More Steps

Simplify
(30z)2−10
Rewrite the expression
More Steps

Evaluate
(30z)2
To raise a product to a power,raise each factor to that power
302z2
Evaluate the power
900z2
900z2−10
900z2−10=0
Move the constant to the right-hand side and change its sign
900z2=0+10
Removing 0 doesn't change the value,so remove it from the expression
900z2=10
Divide both sides
900900z2=90010
Divide the numbers
z2=90010
Cancel out the common factor 10
z2=901
Take the root of both sides of the equation and remember to use both positive and negative roots
z=±901
Simplify the expression
More Steps

Evaluate
901
To take a root of a fraction,take the root of the numerator and denominator separately
901
Simplify the radical expression
901
Simplify the radical expression
More Steps

Evaluate
90
Write the expression as a product where the root of one of the factors can be evaluated
9×10
Write the number in exponential form with the base of 3
32×10
The root of a product is equal to the product of the roots of each factor
32×10
Reduce the index of the radical and exponent with 2
310
3101
Multiply by the Conjugate
310×1010
Multiply the numbers
More Steps

Evaluate
310×10
When a square root of an expression is multiplied by itself,the result is that expression
3×10
Multiply the terms
30
3010
z=±3010
Separate the equation into 2 possible cases
z=3010z=−3010
Solution
z1=−3010,z2=3010
Alternative Form
z1≈−0.105409,z2≈0.105409
Show Solution
