Simplifying Radicals, 4

Category: Algebra

"Published in Newark, California, USA"

Simplify

Solution:

Consider the given equation above

This equation is considered a difficult one because the index of a radical is 6. We need to think a number that is raised to the sixth power will give an answer of 576. If 2 raised to the sixth power, the answer is 64. If 3 raised to the sixth power, the answer is 729. We cannot use 3 because 729 is greater than 576.

If we divide 576 by 2, the answer is 288. Again, if we divide 288 by 2, the answer is 144. The factors of 576 are 4 and 144. 4 and 144 are perfect squares. We can rewrite the above equation as follows

As you noticed that the exponent of 2 is a multiple of 6 while the exponent of x is not. We need to factor and rewrite x into a multiple of 6 as follows

Take the sixth root of the terms with exponents that are multiples of 6, we have

The remaining terms inside the radical have even exponents. Since the index of a radical is 6, we need to further simplify the radical as follows

Therefore, the final answer is

 

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