## Sunday, June 30, 2013

### Algebraic Operations - Radicals, 15

Category: Algebra

"Published in Newark, California, USA"

Perform the indicated operations

Solution:

Consider the given equation above

If you will cube a radical in which the index is 2 or that have a square root sign, then the terms inside the square root sign will be raised to a third power.

If you will multiply a radical with another radical with the same index, then the terms inside the radicals will be multiplied together. In this case, the given above equation can be written as follows

Apply the principles of Binomial Theorem or squaring of a binomial to the above equation as follows

At the first term, x3 is not a perfect square, the factors of x3 are x2 and x. x2 is a perfect square.

At the second term, x2 is a perfect square. The square root of x2 is x.

At the third term, 4y2 is a perfect square. The square root of 4y2 is 2y.

At the fourth term, 8y3 is not a perfect square, the factors of 8y3 are 4y2 and 2y. 4y2 is a perfect square.

Hence, the given equation above becomes

## Saturday, June 29, 2013

### Algebraic Operations - Radicals, 14

Category: Algebra

"Published in Newark, California, USA"

Perform the indicated operations

Solution:

Consider the given equation above

If you will square a radical in which the index is 2 or that have a square root sign, then the square root sign in the equation will be cancelled.

If you will multiply a radical with another radical with the same index, then the terms inside the radicals will be multiplied together. In this case, the given above equation can be written as follows

Apply the principles of Binomial Theorem or squaring of a binomial to the above equation as follows

## Friday, June 28, 2013

### Algebraic Operations - Radicals, 13

Category: Algebra

"Published in Suisun City, California, USA"

Perform the indicated operations

Solution:

Consider the given equation above

If you will multiply a radical with another radical with the same index, then the terms inside the radicals will be multiplied together. In this case, the given above equation can be written as follows

Apply the distributive property of multiplication over addition, as follows

## Thursday, June 27, 2013

### Algebraic Operations - Radicals, 12

Category: Algebra

"Published in Suisun City, California, USA"

Perform the indicated operations

Solution:

Consider the given equation above

If you will multiply a radical with another radical with the same index, then the terms inside the radicals will be multiplied together. In this case, the given above equation can be written as follows

Apply the distributive property of multiplication over addition, as follows

## Wednesday, June 26, 2013

### Algebraic Operations - Radicals, 11

Category: Algebra, Arithmetic

"Published in Suisun City, California, USA"

Perform the indicated operation

Solution:

Consider the given equation above

If you will cube a radical in which the index is 3 or that have a cube root sign, then the cube root sign in the equation will be cancelled.

If you will multiply a radical with another radical with the same index, then the terms inside the radicals will be multiplied together. In this case, the given above equation can be written as follows

Although the above equation consists of numbers only, then we need to apply the principles of Binomial Theorem or cubing of a binomial because the radicals are treated as variables.

## Tuesday, June 25, 2013

### Algebraic Operations - Radicals, 10

Category: Algebra, Arithmetic

"Published in Suisun City, California, USA"

Perform the indicated operations

Solution:

Consider the given equation above

If you will cube a radical in which the index is 2 or that have a square root sign, then the terms inside the square root sign will be raised to a third power.

If you will multiply a radical with another radical with the same index, then the terms inside the radicals will be multiplied together. In this case, the given above equation can be written as follows

Although the above equation consists of numbers only, then we need to apply the principles of Binomial Theorem or cubing of a binomial because the radicals are treated as variables.

At the first term, 33 or 27 is not a perfect square. The factors of 27 are 9 and 3. 9 is a perfect square.

At the second term, 32 or 9 is a perfect square. The square root of 9 is 3.

Hence, the given equation above becomes