Question

How do you solve $ \sqrt {8k} = k $ ?

Answer 1

Hint: In order to solve and write the expression into the simplest form . The square root is related to figuring out what should be the number which when multiplied by itself is equal to the number under the square root symbol $ \sqrt {} $ . This symbol is known as radical . Since in our case we have given the question in which we have to solve and find the value of x , we will first get rid of the radical and remove the square root as we want the original value of x . After eliminating the radical , we will then solve the equation by applying the identity and find the value of the x .

Complete step-by-step answer:
If we see the question , we need to solve the given expression under square root which is $ \sqrt {8k} = k $ . -----equation 1
By applying the concept of equivalent equation , we will first do squaring both sides on $ \sqrt {8k} = k $ both the L . H . S . and the R . H . S . as follows –
We are going to isolate a square root on the L . H . S . So that we can apply the identity as stated below –
 $ \sqrt {8k} = k $
 $ {\left( {\sqrt {8k} } \right)^2} = {\left( k \right)^2} $
After squaring we get ,
 $\Rightarrow 8k = {k^2} $
Now we will solve the quadratic equation ,
Rearranging and writing it sophisticatedly we get –
 $\Rightarrow 0 = {k^2} - 8k $
The factors of this equation will be
Which will give us the two roots as \[{k_1} = 8,{k_2} = 0\]
For verification , we can check the roots by substituting in the original equation ,
 $\Rightarrow \sqrt {8k} = k $
Keeping k=8 as ,
Which is correct .
Keeping k = 0 ,
This is also satisfying .
Therefore , the final answer is \[{k_1} = 8,{k_2} = 0\].
So, the correct answer is “\[{k_1} = 8,{k_2} = 0\]”.

Note: Always remember the algebraic identities .
Always try to get rid of the square root .
We can use prime factorisation for the number inside the radical and pull out non- radical terms or perfect squares from the inside of the square root to make the solution easier .
: In equivalent equations which have identical solutions we can perform multiplication or division by the same non-zero number both L.H.S. and R.H.S. of an equation .
In an equivalent equation which has an identical solution we can raise the same odd power to both L.H.S. and R.H.S. of an equation .
Cross check the answer and always keep the final answer simplified .