<span>
<span>first off your answer is 21.90 and the step by step i wrote it for you:) Finding the
square root of a number is the inverse
operation of squaring that number. Remember, the square of a number
is that number times itself. </span>
The perfect
squares are the squares of the whole numbers.
The square root
of a number, n, written below is the number that gives n when multiplied by
itself.
</span> <span>Many mathematical
operations have an inverse, or opposite, operation. Subtraction is the opposite
of addition, division is the inverse of multiplication, and so on. Squaring,
which we learned about in a previous lesson (exponents),
has an inverse too, called "finding the square root." Remember, the
square of a number is that number times itself. The perfect squares are the
squares of the whole numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 … </span>
The square root
of a number, n, written
<span>
is the number that gives n when multiplied by itself. For example,</span>
<span>because
10 x 10 = 100</span>
Examples
Here are the
square roots of all the perfect squares from 1 to 100.
Finding square
roots of of numbers that aren't perfect squares without a calculator
1. Estimate
- first, get as close as you can by finding two perfect square roots your
number is between.
2. Divide -
divide your number by one of those square roots.
3. Average - take the average of the result of step 2 and the root. <span>4. Use the result of step 3 to repeat steps 2 and 3 until you have a number that is accurate enough for you.
</span> Example: Calculate the square root of 10 () to 2 decimal places. <span>1. Find the two perfect square numbers it lies between.
</span> <span><span>Solution:
</span><span>32 = 9 and 42 = 16, so lies between 3 and 4.</span></span> <span>2. Divide 10 by 3. 10/3 = 3.33 (you can round off your answer)</span> <span>3. Average 3.33 and 3. (3.33 + 3)/2 = 3.1667</span> <span>Repeat step 2: 10/3.1667 = 3.1579</span><span>Repeat step 3: Average 3.1579 and 3.1667. (3.1579 + 3.1667)/2 = 3.1623</span> Try the answer --> Is 3.1623 squared equal to 10? 3.1623 x 3.1623 = 10.0001 If this is accurate enough for you, you can stop! Otherwise, you can repeat steps 2 and 3. <span>Note: There are a number of ways to calculate square roots without a calculator. This is only one of them.</span> <span><span>
</span> </span>
<span> <span />Example: Calculate the square root of 10 () to 2 decimal places. <span>1. Find the two perfect square numbers it lies between.
</span> <span><span>Solution:
</span><span>32 = 9 and 42 = 16, so lies between 3 and 4.</span></span> <span>2. Divide 10 by 3. 10/3 = 3.33 (you can round off your answer)</span> <span>3. Average 3.33 and 3. (3.33 + 3)/2 = 3.1667</span> <span>Repeat step 2: 10/3.1667 = 3.1579
Repeat step 3: Average 3.1579 and 3.1667. (3.1579 + 3.1667)/2 = 3.1623</span> <span>Try the answer --> Is 3.1623 squared equal to 10? 3.1623 x 3.1623 = 10.0001</span> If this is accurate enough for you, you can stop! Otherwise, you can repeat steps 2 and 3. </span> <span> <span><span> <span> </span></span></span></span>
3. Average - take the average of the result of step 2 and the root. <span>4. Use the result of step 3 to repeat steps 2 and 3 until you have a number that is accurate enough for you.
</span> Example: Calculate the square root of 10 () to 2 decimal places. <span>1. Find the two perfect square numbers it lies between.
</span> <span><span>Solution:
</span><span>32 = 9 and 42 = 16, so lies between 3 and 4.</span></span> <span>2. Divide 10 by 3. 10/3 = 3.33 (you can round off your answer)</span> <span>3. Average 3.33 and 3. (3.33 + 3)/2 = 3.1667</span> <span>Repeat step 2: 10/3.1667 = 3.1579</span><span>Repeat step 3: Average 3.1579 and 3.1667. (3.1579 + 3.1667)/2 = 3.1623</span> Try the answer --> Is 3.1623 squared equal to 10? 3.1623 x 3.1623 = 10.0001 If this is accurate enough for you, you can stop! Otherwise, you can repeat steps 2 and 3. <span>Note: There are a number of ways to calculate square roots without a calculator. This is only one of them.</span> <span><span>
</span> </span>
<span> <span />Example: Calculate the square root of 10 () to 2 decimal places. <span>1. Find the two perfect square numbers it lies between.
</span> <span><span>Solution:
</span><span>32 = 9 and 42 = 16, so lies between 3 and 4.</span></span> <span>2. Divide 10 by 3. 10/3 = 3.33 (you can round off your answer)</span> <span>3. Average 3.33 and 3. (3.33 + 3)/2 = 3.1667</span> <span>Repeat step 2: 10/3.1667 = 3.1579
Repeat step 3: Average 3.1579 and 3.1667. (3.1579 + 3.1667)/2 = 3.1623</span> <span>Try the answer --> Is 3.1623 squared equal to 10? 3.1623 x 3.1623 = 10.0001</span> If this is accurate enough for you, you can stop! Otherwise, you can repeat steps 2 and 3. </span> <span> <span><span> <span> </span></span></span></span>
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