Understanding Principal Square Roots

The video tutorial explains how to evaluate principal square roots using real numbers. It covers the concept of the radicand and the conditions under which a square root is real or non-real. Through examples, it demonstrates the calculation of square roots for numbers like 4, 49, and 81, including handling negative square roots. The tutorial concludes with an example of a non-real square root, emphasizing that a negative radicand results in a non-real number.

What is the principal square root of a squared number?

• A non-negative number that when squared equals the original number

• A negative number that when squared equals the original number

• Any number that when squared equals the original number

• A complex number that when squared equals the original number

How can the square root operation be described in relation to squaring?

• As an addition operation

• As a division operation

• As a multiplication operation

• As the inverse of squaring

What is the square root of 4?

• 4

• 1

• 2

• 3

Why is the square root of 49 equal to 7?

• Because 7 is a prime number

• Because 7 squared equals 49

• Because 49 is an even number

• Because 49 is a perfect cube

What is the square root of 49 expressed in terms of multiplication?

• Square root of 8 times 8

• Square root of 7 times 7

• Square root of 5 times 5

• Square root of 6 times 6

What is the result of the negative square root of 81?

• 81

• 9

• -9

• 0

Why is the square root of 81 simplified to 9?

• Because 9 is a prime number

• Because 9 squared equals 81

• Because 81 is a perfect cube

• Because 81 is an even number

Why is the square root of negative twenty-five not a real number?

• Because negative twenty-five is an odd number

• Because there is no non-negative real number squared that equals a negative number

• Because negative twenty-five is not a perfect square

• Because negative numbers cannot have square roots

What happens when the radicand of a square root is negative?

• The result is never a real number

• The result is always a positive number

• The result is always zero

• The result is always a real number

What should be entered if the square root of a number is not real?

• Negative

• Zero

• D

• Infinity