Before we begin, let"s understand the meaning of the square root. The price square source is composed as **√** and is one integral component of mathematics. Once you recognize the basics of finding the square source of a number, you can solve any kind of square root-related problem. In this brief lesson, we will learn about the square root of 48 and find it with different methods like long division method. Let us see what the square root of 48 is.

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**Square root of 48**:

**√**48 = 6.928

**Square of 48: 482**= 2304

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

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

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

4. | FAQs top top Square root of 48 |

The square source of a number is the number the gets multiply to chin to give the product. The square source of 48 is 6.92820323. Square root of 48 in the radical form is express as **√**48 and also in exponent form, that is expressed together 481/2. The square source of 48 rounded to 5 decimal locations is 6.9282...

48 is no a perfect square. We can find the square root of 48 by the approximation method. For the exact value, we deserve to use the long division method. In the approximation method, we find square numbers close to 48. We check out that 36 and 49 are the perfect square numbers close come 48. The square source of 36 is 6 and the square root of 49 is 7. Therefore the square source of 48 must lie between 6 and 7 and more close to 7 as 48 is closer to 49. This an approach only offers us an approximate answer. To recognize the precise value we have the right to use the long division method and also find a more accurate decimal value 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, us take one number from each pair the the very same numbers indigenous its prime factorization and we multiply them. The factorization of 48 is 2 × 3 × 2 × 2 × 2 which has 1 pair of the very same number. It can additionally be created as 48 = 24 × 31. Thus, the easiest radical kind of **√**48 is 4**√**3 itself.

Let united state follow the steps to discover the square source of 48 by lengthy division.

**Step 1**: starting from the right, we will certainly pair increase the number by putting a bar over them.

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

**Step 3**: Now twin the divisor. Guess: v the largest possible digit which will additionally become the brand-new digit in the quotient, together that as soon as the brand-new divisor is multiplied to the brand-new quotient the product is less than or same to the dividend. Divide and write the remainder.

**Explore Square roots making use of 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 root of 48 to its shortest radical form.

**Solution**

We need to express 48 as the product the 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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