Estimating irrational numbers worksheet :
Worksheet on estimating irrational numbers is much useful to the students who would like to practice problems on irrational numbers.
1. Estimate the value of the irrational number √2.
2. Draw a number line and locate your estimation of √2.
3. How could you find an even better estimate of √2 ?
4. Find a better estimate of √2 . Draw a number line and locate and label your estimate.
5. Find a better estimate of √7 . Draw a number line and locate and label your estimate.
Question 1 :
Estimate the value of the irrational number √2.
A. Since 2 is not a perfect square, √2 is irrational.
B. To estimate √2 , first find two consecutive perfect squares that 2 is between. We can do this by writing the following inequality.
1 < 2 < 4
C. Now take the square root of each number.
D. Simplify the square roots of perfect squares.
√2 is between 1 and 2
E. Estimate that √2 ≈ 1.5.
F. To find a better estimate, first choose some numbers between 1 and 2 and square them.
For example, choose 1.3, 1.4, and 1.5.
1.3² = 1.69, 1.4² = 1.96, 1.5² = 2.25
Is √2 between 1.3 and 1.4 ? How do we know ?
No ; √2 is not between 1.69 and 1.96.
Is √2 between 1.4 and 1.5 ? How do we know ?
Yes ; √2 is between 1.96 and 2.25.
Since √2 is between 1.4 and 1.5, we have √2 ≈ 1.45.
Question 2 :
Draw a number line and locate your estimation of √2.
Question 3 :
How could you find an even better estimate of √2 ?
Test the squares of numbers between 1.4 and 1.5.
Question 4 :
Find a better estimate of √2 . Draw a number line and locate and label your estimate.
√2 is between 1.41 and 1.42. So, √2 ≈ 1.415.
Question 5 :
Find a better estimate of √7 . Draw a number line and locate and label your estimate.
√7 is between 2.6 and 2.7. So, √7 ≈ 2.65.
After having gone through the stuff given above, we hope that the students would have understood "Worksheet on estimating irrational numbers".
Apart from the stuff given above, if you want to know more about "Estimating irrational numbers", please click here
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
MATH FOR KIDS
HCF and LCM word problems
Word problems on quadratic equations
Word problems on comparing rates
Ratio and proportion word problems
Converting repeating decimals in to fractions