
How do you simplify without using a calculator?
Answer
462.3k+ views
Hint: We will equate the given value to a variable Then, we will square the whole equation. Later, we will try to find the square root of the value in the tenth and hundredth decimal places.
Complete step by step answer:
Consider the given value which is the square root of a decimal number.
We are supposed to equate the given value to a variable, say
By this procedure, we will get
Now we are going to square and so, we will square the given value, because they both are equal.
We will get
Now, let us consider the digits after the decimal point. We have in the tenth decimal place and in the hundredth decimal place.
Let us just keep the decimal point away.
So, we have the two digit number
Without any doubt we can say that is a perfect square.
And hence we will get
Here, we have the number
That is, there are two decimal positions in the number. That means the root will be a number which has only one decimal position.
So, we will get
We will get
So, we will get
Now we know that the square root and the square act as inverse operations when they act together on a number.
Thus, we will get
Hence
Note: We know that if we multiply two decimal numbers, then
First: we remove the decimal points of both the numbers.
Second: we multiply the whole numbers.
Third: we count the number of digits in the decimal positions of both the numbers.
Fourth: we count the digits of the product from the right side to see where we need to put the decimal point. The number of decimal positions in the product is equal to the sum of the number of decimal positions in both numbers to be multiplied.
Complete step by step answer:
Consider the given value
We are supposed to equate the given value to a variable, say
By this procedure, we will get
Now we are going to square
We will get
Now, let us consider the digits after the decimal point. We have
Let us just keep the decimal point away.
So, we have the two digit number
Without any doubt we can say that
And hence we will get
Here, we have the number
That is, there are two decimal positions in the number. That means the root will be a number which has only one decimal position.
So, we will get
We will get
So, we will get
Now we know that the square root and the square act as inverse operations when they act together on a number.
Thus, we will get
Hence
Note: We know that if we multiply two decimal numbers, then
First: we remove the decimal points of both the numbers.
Second: we multiply the whole numbers.
Third: we count the number of digits in the decimal positions of both the numbers.
Fourth: we count the digits of the product from the right side to see where we need to put the decimal point. The number of decimal positions in the product is equal to the sum of the number of decimal positions in both numbers to be multiplied.
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