Question
Calculate the value
5052−1
Alternative Form
≈0.121421
Evaluate
(1002)(1−501)
Cancel out the common factor 2
(501)(1−501)
Simplify the root
More Steps

Evaluate
501
To take a root of a fraction,take the root of the numerator and denominator separately
501
Simplify the radical expression
501
Simplify the radical expression
More Steps

Evaluate
50
Write the expression as a product where the root of one of the factors can be evaluated
25×2
Write the number in exponential form with the base of 5
52×2
The root of a product is equal to the product of the roots of each factor
52×2
Reduce the index of the radical and exponent with 2
52
521
Multiply by the Conjugate
52×22
Multiply the numbers
More Steps

Evaluate
52×2
When a square root of an expression is multiplied by itself,the result is that expression
5×2
Multiply the terms
10
102
102(1−501)
Simplify the root
More Steps

Evaluate
501
To take a root of a fraction,take the root of the numerator and denominator separately
501
Simplify the radical expression
501
Simplify the radical expression
More Steps

Evaluate
50
Write the expression as a product where the root of one of the factors can be evaluated
25×2
Write the number in exponential form with the base of 5
52×2
The root of a product is equal to the product of the roots of each factor
52×2
Reduce the index of the radical and exponent with 2
52
521
Multiply by the Conjugate
52×22
Multiply the numbers
More Steps

Evaluate
52×2
When a square root of an expression is multiplied by itself,the result is that expression
5×2
Multiply the terms
10
102
102(1−102)
Subtract the numbers
More Steps

Simplify
1−102
Reduce fractions to a common denominator
1010−102
Write all numerators above the common denominator
1010−2
102×1010−2
To multiply the fractions,multiply the numerators and denominators separately
10×102×(10−2)
Multiply the numbers
More Steps

Evaluate
2×(10−2)
Apply the distributive property
2×10−2×2
Multiply the numbers
102−2×2
When a square root of an expression is multiplied by itself,the result is that expression
102−2
10×10102−2
Multiply the numbers
100102−2
Rewrite the expression
1002(52−1)
Solution
5052−1
Alternative Form
≈0.121421
Show Solution
