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Square Root of 74

Square root of 74 is the value which, when multiplied by itself, gives the original number. Let's explore to find the square root of 74. Since 74 isn't a perfect square, the square root will be an irrational number. Also, check out the solved examples on square root of 74 and try your hand at solving a few interactive questions at the end of the page. In this lesson, you will learn different methods to find the square root of 74.

Square of 74: 74² = 5476
Square Root of 74:√74 = 8.602

1.	What Is the Square Root of 74?
2.	Is Square Root of 74 Rational or Irrational?
3.	How to Find the Square Root of 74?
4.	Important Notes on Square Root of 74
5.	FAQs on Square Root of 74
6.	Challenging Questions

What is the square root of 74?

The square root of 74 is 8.602 and expressed as √74=8.6

square root of 74

The square root of 74 lies between the whole numbers 8 and 9

Is Square Root of 74 Rational or Irrational?

The square root of 74 is a non-terminating decimal.
√74=8.60232526704..
Also, it cannot be expressed in the form of a fraction (p/q), and hence is an irrational number.

How to Find Square Root of 74?

The square root of 74 can be easily calculated by long division.

Square root of 74 by Long Division

At each step of the long division, the quotient is added to the divisor. Also, two digits (two zero's) are carried over in each step of the division process. The method of long division method gives an exact value of the square root. Further using this long division, the square root values of a few numbers are:

Important Notes:

The square root of 74 in the radical form is expressed as √74.
In exponent form, the square root of 74 is expressed as 74^½.

Challenging Question

A school has about 744 students. On a sports meet, the teachers wish to make the students stand in columns, such that the number of students in each column is equal to the number of columns. Find the number of students in each column with the help of techniques used in square root of 74.

Example 1 Susan has a list of 74 guests for a party She has to make the arrangement of chairs, such that the number of rows is equal to the number of chairs in each row. Find the number of chairs in each row.

Solution

Given that Susan has 74 guests.
Also we have:
Number of rows = Number of chairs in each row = x
Total chairs = Number of rows x Number of chairs in each row
Total chairs = x × x = x²
We know that square root of 74 s not a perfect square. Let us try to find the number which is nearest to 74 and is a perfect square.
The square number greater than 74 is 81
Hence x²= 81 = x = 9
Example 2 A group plans for an excursion for its members and decides to collect as much money from each member as the number of members in the group. The total amount collected is $.5476 How many members are there in the group.

Solution

Given that the number of members in the group is equal to the amount of money collected from each member.
Number of member in the group = Amount collected from each member = x
Total amount collected = $5476
Number of members × Amount collected from each member = $5476
x × x = 5476
x²= 5476
x = √5476 = 74
$74 is collected from each member of the group.

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FAQs on Square Root of 74

Can Square Root 74 be simplified?

The square root of 74 cannot be simplified into integers but can be simplified in decimals in approximate values.

Is the square root of 74 rational or irrational?

The square root of 74 is an irrational number because it can not be expressed in fractions.

What is the square root of 74 rounded to the nearest tenth?

The square root of 74 rounded to the nearest tenth is 8.6.

Is 74 a perfect square?

74 is not a perfect square.

What is the square root of 74 up to 3 decimal places?

Square root of 74 up to 3 decimal places is 8.602.

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