Answer
Verified
425.1k+ views
Hint:At first, we have to find the factors of \[900\]. From them we will find the two equal factors for which the product is \[900\].
A factor is a number that divides into another number exactly and without leaving a remainder.
Complete step-by-step answer:
It is given that: The number is \[900\].
The factors of \[900\] are: \[
1,{\text{ }}2,{\text{ }}3,{\text{ }}4,{\text{ }}5,{\text{ }}6,{\text{ }}9,{\text{ }}10,{\text{ }}12,{\text{ }}15,{\text{ }}18,{\text{ }}20,{\text{ }}25,{\text{ }}30,{\text{ }}36,{\text{ }}45,{\text{ }}50,{\text{ }}60,\;75,{\text{ }}90,{\text{ }}100,{\text{ }}150,{\text{ }}180,{\text{ }}225,\,{\text{ }} \\
300,{\text{ }}450,\;900. \\
\]
\[900\] has twenty-seven factors. Among them we have to find the two equal factor for which the product is \[900\].
Let us take \[x\] to be the equal factor of \[900\] such that it gives the product as \[900\].
According to the problem,
\[x \times x = 900\]
Simplifying we get,
\[{x^2} = 900\]
Taking square root of both the sides we get,
\[x = \sqrt {900} = 30\]
Square root of any number gives two values: a positive value and a negative value.
Here, we will take only the positive value. Because, a negative number cannot be a factor of a positive number.
Hence, the equal factor is \[30.\]
Note:Multiplying two whole numbers gives a product. The numbers that we multiply are the factors of the product.
The factors divide a number completely without leaving any remainder.
Square root of any number gives two values: a positive value and a negative value.
Here, we will take only the positive value. Because, a negative number can not be a factor of a positive number.
If we divide a positive number and a negative number the quotient will be a negative number. So, we cannot take \[ - 30\] as the factor.
A factor is a number that divides into another number exactly and without leaving a remainder.
Complete step-by-step answer:
It is given that: The number is \[900\].
The factors of \[900\] are: \[
1,{\text{ }}2,{\text{ }}3,{\text{ }}4,{\text{ }}5,{\text{ }}6,{\text{ }}9,{\text{ }}10,{\text{ }}12,{\text{ }}15,{\text{ }}18,{\text{ }}20,{\text{ }}25,{\text{ }}30,{\text{ }}36,{\text{ }}45,{\text{ }}50,{\text{ }}60,\;75,{\text{ }}90,{\text{ }}100,{\text{ }}150,{\text{ }}180,{\text{ }}225,\,{\text{ }} \\
300,{\text{ }}450,\;900. \\
\]
\[900\] has twenty-seven factors. Among them we have to find the two equal factor for which the product is \[900\].
Let us take \[x\] to be the equal factor of \[900\] such that it gives the product as \[900\].
According to the problem,
\[x \times x = 900\]
Simplifying we get,
\[{x^2} = 900\]
Taking square root of both the sides we get,
\[x = \sqrt {900} = 30\]
Square root of any number gives two values: a positive value and a negative value.
Here, we will take only the positive value. Because, a negative number cannot be a factor of a positive number.
Hence, the equal factor is \[30.\]
Note:Multiplying two whole numbers gives a product. The numbers that we multiply are the factors of the product.
The factors divide a number completely without leaving any remainder.
Square root of any number gives two values: a positive value and a negative value.
Here, we will take only the positive value. Because, a negative number can not be a factor of a positive number.
If we divide a positive number and a negative number the quotient will be a negative number. So, we cannot take \[ - 30\] as the factor.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Why Are Noble Gases NonReactive class 11 chemistry CBSE
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
At which age domestication of animals started A Neolithic class 11 social science CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Write a letter to the principal requesting him to grant class 10 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE