Is is square root of 1.6875 a rational number

Mathematics

1 answer:

mamaluj [8]3 years ago

4 0

Question:

Is square root of 1.6875 a rational number ?

Answer:

Square root of 1.6875 a rational number is not a rational number

Solution:

Given that we have to find square root of 1.6875 and determine if it is rational number or not

Let us first find square root of 1.6875

$\sqrt{1.6875} = 1.29903810568$

Let us understand about rational number

A rational number is a number that can be expressed as a fraction (ratio) in the form $\frac{p}{q}$ where p and q are integers and q is not zero.

When a rational number fraction is divided to form a decimal value, it becomes a terminating or repeating decimal.

So the number 1.29903810568 is not a rational number

In other words we can say,

Only the square roots of square numbers are rational. Here 1.6875 is not a perfect square. So it is not rational number

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A fair die is rolled twice. What is the probability that: a. The die shows a different number on each toss. e.g. (2,5) b. The su

Eduardwww [97]

Answer:

a) $\frac{5}{6}$

b) $\frac{1}{6}$

c) $\frac{1}{9}$

Step-by-step explanation:

Total possible outcomes when a dice is rolled twice

(1,1) , (1,2) , (1,3) , (1,4) , (1,5) , (1,6)

(2,1) , (2,2) , (2,3) , (2,4) , (2,5) , (2,6)

(3,1) , (3,2) , (3,3) , (3,4) , (3,5) , (3,6)

(4,1) , (4,2) , (4,3) , (4,4) , (4,5) , (4,6)

(5,1) , (5,2) , (5,3) , (5,4) , (5,5) , (5,6)

(6,1) , (6,2) , (6,3) , (6,4) , (6,5) , (6,6)

here total number of possible outcomes is 36

now,

P (Event ) = $\frac{\textup{Number of favorable outcomes of an Event}}{\textup{Total possible outcomes}}$

a) P( die shows a different number on each toss )

Favorable outcomes = (1,2) , (1,3) , (1,4) , (1,5) , (1,6) , (2,1) , (2,3) , (2,4) , (2,5) , (2,6), (3,1) , (3,2) , (3,4) , (3,5) , (3,6) , (4,1) , (4,2) , (4,3) , (4,5) , (4,6) , (5,1) , (5,2) , (5,3) , (5,4) , (5,6) , (6,1) , (6,2) , (6,3) , (6,4) , (6,5)

number of Favorable outcomes = 30

thus,

P( die shows a different number on each toss ) = $\frac{30}{36}=\frac{5}{6}$