Understanding Squaring of Sums and Differences Involving Radicals

The video tutorial explains how to square sums and differences involving radicals, specifically square roots. It emphasizes that there are no shortcuts, and the expressions must be expanded and multiplied using methods like FOIL or double distribution. Two examples are provided: one for squaring a sum and another for squaring a difference. Each example is broken down step-by-step, showing how to distribute terms, combine like terms, and simplify the results. The tutorial concludes by reiterating the importance of expanding expressions fully when dealing with radicals.

What is the main concept to remember when squaring sums and differences involving radicals?

• There are shortcuts available.

• You must expand and multiply.

• You can square each term separately.

• You should only focus on the first term.

In the first example, what is the result of multiplying the square root of 11 by itself?

• Square root of 22

• 11

• Square root of 121

• 22

How do you combine like terms in the expression 9 square root of 11 + 9 square root of 11?

• 11 square root of 9

• 81

• 9 square root of 22

• 18 square root of 11

What is the final simplified expression for the first example?

• 92 + 9 square root of 11

• 92 + 18 square root of 11

• 81 + 18 square root of 11

• 81 + 9 square root of 11

In the second example, what is the first product when expanding 2 square root 5 - square root 2?

• 4 square root of 10

• 2 square root of 10

• 2 square root of 5

• 4 square root of 5

What is the result of multiplying negative square root 2 by itself?

• Negative square root of 4

• Square root of 4

• Positive 2

• Negative 2

How do you simplify the expression 4 times the square root of 5 squared?

• 20

• 25

• 4

• 5

What is the final simplified expression for the second example?

• 22 + 4 square root 10

• 20 + 4 square root 10

• 20 - 4 square root 10

• 22 - 4 square root 10

What is the key takeaway when dealing with sums or differences involving square roots?

• Focus only on the first term.

• Always write in expanded form and multiply.

• Use shortcuts to save time.

• Ignore the radicals.

What is the result of combining -2 square root 10 and -2 square root 10?

• 0

• 4 square root 10

• -4 square root 10

• 2 square root 10