**Solve a quadratic equation using square roots :**

Whenever we have a equation like x² = a, we can find the values of x by taking square root on both sides.

Let us see some example problems based on the above concept.

**Example 1 :**

Solve for y

y² = 16

**Solution :**

**To solve the equation **y² = 16, we have to take square roots on both sides.

√y² = √16

On the left side square and root will get canceled. Now on the right side, we will have √16. Since 16 is positive, we will have two real roots.

y = √16

y = √(4 x 4) = ± 4

Hence y = 4 and y = -4.

**Example 2 :**

Solve for x

x² + 8 = 20

**Solution :**

**To solve the above equation, we have to isolate **x², for that we have to subtract 8 on both sides.

x² + 8 - 8 = 28 - 8

x² = 20

Now we have to take square roots on both sides.

√x² = √20

x = √20

Now we have to split 20 as much as possible.

x = √(2 x 2 x 5) = ± 2√5

Hence x = 2√5 and x = -2√5

**Example 3 :**

Solve for x

2x² = -72

**Solution :**

**To solve the above equation, we have to isolate **x², for that we have to divide by 2 on both sides.

2x²/2 = -72/2

x² = -36

Now we have to take square roots on both sides.

√x² = √-36

x = √-36

Since the number inside the radical sign is negative, we will have two imaginary roots.

x = i√36

Now we have to split 36 as much as possible.

x = i√(2 x 2 x 3 x 3) = ± i (2 x 3) = ±6i

Hence x = 6i and x = -6i

**Example 4 :**

Solve for t

-5t² = -500

**Solution :**

**To solve the above equation, we have to isolate t**², for that we have to divide by (-5) on both sides.

-5x²/(-5) = -500/(-5)

x² = 100

Now we have to take square roots on both sides.

√x² = √100

x = √100

Since the number inside the radical sign is positive, we will have two real roots.

Now we have to split 100 as much as possible.

x = √(2 x 2 x 5 x 5) = ± (2 x 5) = ± 10

Hence x = 10 and x = -10

**Example 5 :**

Solve for x

9x² + 10 = 91

**Solution :**

**To solve the above equation, we have to isolate t**², for that we have to subtract 10 on both sides.

9x² + 10 - 10 = 91 - 10

9x² = 81

Divide 9 on both sides

9x²/9 = 81/9

x²= 9

Now we have to take square roots on both sides.

√x² = √9

x = √9

Since the number inside the radical sign is positive, we will have two real roots.

Now we have to split 9 as much as possible.

x = √(3 x 3) = ±3

Hence x = 3 and x = -3

After having gone through the stuff given above, we hope that the students would have understood "Solve a quadratic equation using square roots".

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