# What were the three famous problems of antiquity?

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### Table of contents:

- What were the three famous problems of antiquity?
- What are the three Greek problems of antiquity?
- Which of the following is associated with the famous impossible Delian problem?
- Why is doubling cubes impossible?
- Is doubling a square possible or impossible?
- Why is squaring a circle impossible?
- What is doubling a square?
- Is it possible to construct a cube of twice the volume?
- What is the cube double of A?
- What happens when side of a square is doubled?
- What is the double square root of 16?
- What is double the square root of 3?
- Is √ 3 an irrational number?
- Why is √ 3 an irrational number?
- What is the root square of 10?
- What is the root square of 169?
- Why is 9 The square root of 81?

## What were the three famous problems of antiquity?

The **three classical** construction **problems of antiquity** are known as ``squaring the circle'', ``trisecting an angle'', and ``doubling a cube''. Here is a short description of each of these **three problems**: Squaring the Circle. Given a circle, construct a square that has exactly the same area as the circle.

## What are the three Greek problems of antiquity?

years after they were formulated, were all **three** ancient **problems** proved insoluble using only compass and straightedge....**The Greek problems of antiquity were a set of geometric problems whose solution was sought using only compass and straightedge:**

- circle squaring.
- cube duplication.
- angle trisection.

## Which of the following is associated with the famous impossible Delian problem?

If you are doing Apex, the answer is doubling a cube. It can't be done with a straightedge or compass so it is **impossible** and was believed to be Apollo wanted something of his doubled with was a cube.

## Why is doubling cubes impossible?

This is because a **cube** of side length 1 has a volume of 13 = 1, and a **cube** of twice that volume (a volume of 2) has a side length of the **cube** root of 2. The impossibility of **doubling** the **cube** is therefore equivalent to the statement that 3√2 is not a constructible number.

## Is doubling a square possible or impossible?

By geometric construction, **Doubling** a cube is not **possible**, as Cube is already a 3 D figure and after **doubling** it becomes 6 -D figure which is not **possible** to draw using geometric construction. By geometric construction, **Doubling a square** is **possible**.

## Why is squaring a circle impossible?

Since the area of the **circle** will always be a transcendental number and the area of a **square** has to be an integer, this can never happen in a finite number of steps. Therefore, you cannot **square a circle**. It's a metaphor for that which cannot be done.”

## What is doubling a square?

**Doubling** the Area of a Given **Square**. Why it works: The area of the original **square** is AB^2, so we want a **square** of area 2AB^2. If the side of the new **square** is s, then we want s^2 = 2AB^2, or s = AB*sqrt(2), which is the length of the diagonal of the **square**.

## Is it possible to construct a cube of twice the volume?

No, it is not. That specific question is named the Delian Problem, where supposedly, Apollo, the Greek god, had asked for his altar to be doubled in size to stop a plague going around. The builders only had a compass and straightedge, but they couldn't figure out how to double the **volume**.

## What is the cube double of A?

UPSC Question The Questions and Answers of **What is the cube** of **double** of 'a'? a)16a3b)2ac)8a3d)4a2Correct answer is option 'C'.

## What happens when side of a square is doubled?

Since the **side of a square is doubled**. ⇒New **side** =2a. Area of the **square** =(2a)2=4a2. ∴ Area of the **square** becomes 4 times .

## What is the double square root of 16?

The **square root of 16** is 4. It is the positive solution of the equation x2 = **16**. The number **16** is a perfect **square**....**Square Root of 16** in radical form: √**16**.

1. | What Is the Square Root of 16? |
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4. | FAQs on Square Root of 16 |

## What is double the square root of 3?

It is just another simple multiplication. Just keep the 2 along with √**3** . So that becomes, ⇒2×√**3**=2√**3** .

## Is √ 3 an irrational number?

The **square root** of **3** is an **irrational number**. It is also known as Theodorus' constant, after Theodorus of Cyrene, who proved its irrationality.

## Why is √ 3 an irrational number?

**A rational number** is defined as a **number** that can be expressed in the form of a division of two integers, i.e. p/q, where q is not equal to 0. **√3** = 1.

## What is the root square of 10?

List of Perfect Squares