Simplifying Radicals, 3

Category: Algebra

"Published in Newark, California, USA"

Simplify

Solution:

Consider the given equation above

As you noticed that the numerator has a negative sign. Well, it's fine because the cube root of any negative number is always a negative number. Also, the numerator is not a perfect cube because the exponent of x is not a multiple of 3. We need to factor and rewrite x into a multiple of 3 as follows

Take the cube root of the terms with exponents that are multiples of 3, we have

Next, we need to rationalize the denominator in order to eliminate the radical sign at the denominator by multiplying both the numerator and denominator by 2², we have 

Since the exponents of 2 and x are smaller than the index of a radical, therefore the final answer is

Simplifying Radicals, 2

Category: Algebra

"Published in Newark, California, USA"

Simplify

Solution:

Consider the given equation above 

We can rewrite the above equation as follows

Since the exponents of 2 and x are odd numbers, then factor 2 and x into odd and even exponents as follows

Take the square root of the terms with even exponents, we have

Therefore, the final answer is

Simplifying Radicals

Category: Algebra

"Published in Newark, California, USA"

 Simplify

Solution:

Consider the given equation above

We can rewrite the above equation as follows

 Next, we need to eliminate the radical sign at the denominator by rationalization of the denominator. The exponent of 3 is 2 and the exponent of y is 3. We need to multiply both the numerator and denominator by 3²y as follows

Since the exponent of 3 is 2, the exponent of x is 1, and the exponent of y is 1, then we cannot simplify further because the index of the radical is 4. Therefore, the final answer is

or