Evaluate 8√3cosec²30sin60cos60cos²45sin45tan30cosec45
Answers
The square root of 8 in radical form is represented as √8 which is also equal to 2√2 and as a fraction, it is equal to 2.828 approximately. Squares root of a number is the number, which, on multiplying by itself gives the original number. Since 8 is not a perfect square, hence the value is represented in root form.
The value 2√2 is said to be surd, as it cannot be further simplified. As we all know, 8 = 2 × 2 × 2, thus we can see the number is a perfect cube of 2. So, we can determine the cube root of 8 which is equal to 2, such as 3√8 = 2. But for numbers which are perfect squares such as 4, 9, 16, 25, etc. the root for them can be determined easily, such as;
√4 = √(2 x 2) = 2
√9 = √(3 x 3) = 3
√16 = √(4 x 4) = 4
√25 = √(5 x 5) = 5
Square Root of 8
√8 = 2.82842712475
Or
√8 = 2.828 up to three places of decimal
Now that you know the value of root 8, let us calculate its value here. Although finding the square root of a number by using calculators is very easy, but students should know how to calculate it manually.
The square root is represented by the symbol, ‘√’. This symbol ‘√’ is called a radical symbol or radix. The number underneath the radical symbol or radix is called as radicand.
Method to Find Value of Root 8
To give you an idea, the square of 2 is 4 and the square of 3 is 9. So, the square root of 8 essentially lies between these two digits. But, since 3 square is 9, which is greater than 8, it most probably lies between 2.8 or 2.9. The actual answer for the square root of 8 is 2.82842712475. And this is really close to our estimate. Similarly, you could use this technique to find out square roots of other numbers.
Do you know what the square root of 8 to the power of 3 is? To solve the problem, we need to take the square root of 8. Then, we take that value and multiply by itself 3 times.
So essentially, square root of 8 to the power of 3 = (2.828 x 2.828 x 2.828) = 22.627.
Now, it’s easy to find the square root of 8, and we also learned what square root of 8 to the power of 3 is.
Also learn to find the square root of 6, 7, 9, 10, 11 and 12, by reaching to the below-mentioned links.
Square Root Of 6
Square Root Of 7
Square Root Of 9
Square Root Of 10
Square Root Of 11
Square Root Of 12
Square root Table From 1 to 15
In the table given here, find the values of root of numbers from 1 to 15 to use it for mathematical calculations.
Number Squares Square Root (Upto 3 places of decimal)
1 12 = 1 √1 = 1
2 22 = 4 √2 = 1.414
3 32 = 9 √3 = 1.732
4 42 = 16 √4 = 2.000
5 52 = 25 √5 = 2.236
6 62 = 36 √6 = 2.449
7 72 = 49 √7 = 2.646
8 82 = 64 √8 = 2.828
9 92 = 81 √9 = 3.000
10 102 = 100 √10 = 3.162`
11 112 = 121 √11 = 3.317
12 122 = 144 √12 = 3.464
13 132 = 169 √13 = 3.606
14 142 = 196 √14 = 3.742
hope it helps you｡◕‿◕｡
