Before we begin, let"s understand the definition of the square root. The symbol square root is composed as **√** and is an integral component of mathematics. When you know the basics of detect the square source of a number, you have the right to solve any square root-related problem. In this quick lesson, we will learn about the square root the 48 and discover it with various methods prefer long division method. Let us see what the square source of 48 is.

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**Square source of 48**:

**√**48 = 6.928

**Square the 48: 482**= 2304

1. | What Is the Square root of 48? |

2. | Is Square root of 48 Rational or Irrational? |

3. | How to uncover the Square root of 48? |

4. | FAQs ~ above Square root of 48 |

The square source of a number is the number the gets multiplied to itself to give the product. The square source of 48 is 6.92820323. Square source of 48 in the radical type is express as **√**48 and in exponent form, the is expressed together 481/2. The square source of 48 rounded come 5 decimal areas is 6.9282...

48 is no a perfect square. Us can discover the square root of 48 by the approximation method. For the precise value, we have the right to use the long division method. In the approximation method, we discover square number close to 48. We check out that 36 and 49 are the perfect square numbers close come 48. The square root of 36 is 6 and the square source of 49 is 7. Because of this the square source of 48 must lie in between 6 and 7 and more close come 7 as 48 is closer come 49. This an approach only gives us an approximate answer. To understand the exact value we deserve to use the long division method and find a more accurate decimal worth for **√**48.

### Simplified Radical type of Square source of 48

48 is a composite number. When we find square source of any kind of number, we take one number from each pair the the same numbers from its element factorization and also we main point them. The factorization of 48 is 2 × 3 × 2 × 2 × 2 which has actually 1 pair of the exact same number. It can additionally be written as 48 = 24 × 31. Thus, the most basic radical type of **√**48 is 4**√**3 itself.

Let us follow the actions to discover the square root of 48 by long division.

**Step 1**: beginning from the right, we will certainly pair up the number by placing a bar over them.

**Step 2**: find a number which, when multiplied to itself, offers the product much less than or equal to 48. So, the number is 4. Placing the divisor as 6, we get the quotient together 6 and the remainder 36.

**Step 3**: Now twin the divisor. Assumption: v the largest possible digit i m sorry will additionally become the brand-new digit in the quotient, together that once the brand-new divisor is multiplied to the new quotient the product is much less than or equal to the dividend. Divide and write the remainder.

**Explore Square roots utilizing illustrations and also interactive examples**

**Important Notes:**

**√**48 are 6.928.

**Challenging Questions:**

**√**

**√**48?Determine the square source of -48.

**Example 2**: Help Ross simplify the square source of 48 to its lowest radical form.

**Solution**

We need to express 48 as the product that its prime factors as 48 = 2 × 3 × 2 × 2 × 2.**Therefore, √**48 = **√**(2 × 2 × 2 × 2 × 2) = 4**√**3.**Thus, 4√**3 is in the lowest radical form.

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