How do we find Square Roots?
The square of 5 is 25 because 5² or 5 x 5 = 25
The square of 4 is 16 because 4² or 4 x 4 = 16
The REVERSE process of squaring is finding a SQUARE ROOT?
A square root of 16 is 4 because 4² = 16
A square root of 25 is 5 because 5² = 25
 |
| Radical |
When talking about square roots we use the symbol shown below called a RADICAL sign to name square roots.
 |
| Examples of RADICAL sign and SQUARE ROOTS |
√͞ 49 = 7 because 7² = 49
√͞ 1 = 7 because 1² =1
√͞ 81 = 7 because 9² =81
√͞ 1/36 = 1/6 because 1/6 x 1/6 = 1/36
√͞ 4/25 = 2/5 because 2/5 x 2/5 = 4/25
PRACTICE:
Answers:
a. 10 b. 8 c. 11 d. 0
In the examples shown above we have found PERFECT SQUARES. The reason that we call them perfect squares is because their square root is a WHOLE NUMBER or a FRACTION.
But if we consider a problem like √͞5 we will be able to visualize quickly that the square roots are NOT whole numbers or fractions.
Even though the square root of 5 CANNOT be written as either a whole number OR a fraction it can be APPROXIMATED by estimating its value.
We ESTIMATE such values by using a table OR by using a calculator.
Consider the problem √͞43 ≈ 6.557 and √͞80 ≈ 8.944
 |
| Estimate values WITHOUT use of calculator OR table. |
Without a calculator or a table:
a. Determine which two whole numbers √͞78 is between.
b. Use part a to approximate √͞78 to the nearest whole number.
SOLUTION:
a. Review perfect squares and recall that √͞64 = 8 and √͞81 = 9. Since 78 is between 64 and 81, √͞78 is between √͞64 (or 8) and √͞81 (or 9). THUS √͞78 is between 8 and 9 or apx between 8.75 and 8.9.
NEXT . . .
PYTHAGOREAN THEOREM:
½
dkdkdkdkdk
dkdkd
²
No comments:
Post a Comment