Question

find the square root of each of the following number correct to two decimal places :789​

Answer 1

The square root of 789 is expressed as √789 in the radical form and as (789)½ or (789)0.5 in the exponent form. The square root of 789 rounded up to 10 decimal places is 28.0891438104.

It is the positive solution of the equation

$\\ \\ \\ {x}^{2} = 789$

• Square Root of 789: 28.089143810376278
• Square Root of 789: 28.089143810376278Square Root of 789 in exponential form: (789)½ or (789)0.5
• Square Root of 789: 28.089143810376278Square Root of 789 in exponential form: (789)½ or (789)0.5Square Root of 789 in radical form: √789

What is the Square Root of 789?

• The square root of 789, (or root 789), is the number which when multiplied by itself gives the product as 789. Therefore, the square root of 789 = √789 = 28.089143810376278.

How to Find Square Root of 789?

Explanation:

• Forming pairs: 07 and 89

Find a number Y (2) such that whose square is <= 7. Now divide 07 by 2 with quotient as 2.Bring down the next pair 89, to the right of the remainder 3. The new dividend is now 389.

Add the last digit of the quotient (2) to the divisor (2) i.e. 2 + 2 = 4. To the right of 4, find a digit Z (which is 8) such that 4Z × Z <= 389. After finding Z, together 4 and Z (8) form a new divisor 48 for the new dividend 389.

Divide 389 by 48 with the quotient as 8, giving the remainder = 389 - 48 × 8 = 389 - 384 = 5.

Now, let's find the decimal places after the quotient 28.

• Bring down 00 to the right of this remainder 5.

• The new dividend is now 500.Add the last digit of quotient to divisor i.e. 8 + 48 = 56.

• To the right of 56, find a digit Z (which is 0) such that 56Z × Z <= 500. Together they form a new divisor (560) for the new dividend (500).Divide 500 by 560 with the quotient as 0, giving the remainder = 500 - 560 × 0 = 500 - 0 = 500.Bring down 00 again.

Repeat above steps for finding more decimal places for the square root of 789.Therefore, the square root of 789 by long division method is 28.0 approximately.

Is Square Root of 789 Irrational?

Is Square Root of 789 Irrational?The actual value of √789 is undetermined. The value of √789 up to 25 decimal places is 28.08914381037627853741012. Hence, the square root of 789 is an irrational number.l

Answer 2

then

\: \: \: \: (1) \: tan \theta \: = \: \sqrt{ {r}^{2} - 1}(1)tanθ=

r

2

−1

\: \: \: \: (2) \: cos \theta \: = \: r(2)cosθ=r

\: \: \: \: (3) \:sin \theta \: + cos \theta \: = \: \dfrac{ \sqrt{1 + {r}^{2} } }{r}(3)sinθ+cosθ=

r

1+r

2

\: \: \: \: (4) \: cot \theta \: = \: \sqrt{1 - {r}^{2}}(4)cotθ=

1−r

2

then

\: \: \: \: (1) \: tan \theta \: = \: \sqrt{ {r}^{2} - 1}(1)tanθ=

r

2

−1

\: \: \: \: (2) \: cos \theta \: = \: r(2)cosθ=r

\: \: \: \: (3) \:sin \theta \: + cos \theta \: = \: \dfrac{ \sqrt{1 + {r}^{2} } }{r}(3)sinθ+cosθ=

r

1+r

2

\: \: \: \: (4) \: cot \theta \: = \: \sqrt{1 - {r}^{2}}(4)cotθ=

1−r

2

then

\: \: \: \: (1) \: tan \theta \: = \: \sqrt{ {r}^{2} - 1}(1)tanθ=

r

2

−1

\: \: \: \: (2) \: cos \theta \: = \: r(2)cosθ=r

\: \: \: \: (3) \:sin \theta \: + cos \theta \: = \: \dfrac{ \sqrt{1 + {r}^{2} } }{r}(3)sinθ+cosθ=

r

1+r

2

\: \: \: \: (4) \: cot \theta \: = \: \sqrt{1 - {r}^{2}}(4)cotθ=

1−r

2