Question

(a) Express 146000 in the standard form k x 10n .
(b)Express 155000 in the exponential form.
(c) Find the least number by which 158000 should be divided to make it a perfect square.
(d) Find the square root of 211000 correct upto 2 decimal places.
(e) Find the least number to be subtracted from 216000 to make it a perfect square.

Answer 1

(c) I guess it's ans is 395

Answer 2

Answer:

a) $146000=146\times 10^3$

b) $155000 =155\times 10^3$

c) The least number is 395 by which 158000 should be divided to make it a perfect square.

d) $\sqrt{211000}=459.34$

e) 214564 is the least number to be subtracted from 216000 to make it a perfect square.

Step-by-step explanation:

(a) Express 146000 in the standard form $k\times 10^n$

Solution :

We can re-write 146000 as

$146000=146\times 1000$

or $146000=146\times 10^3$

Where k=146 and n=3

(b)Express 155000 in the exponential form.

Solution :

Exponential form means the equation in power form.

We can re-write 155000  as

$155000 =155\times 1000$

or $155000 =155\times 10^3$

(c) Find the least number by which 158000 should be divided to make it a perfect square.

First we find the prime factor of number 158000

$158000=2\times 2\times 2\times2\times5 \times 5 \times 5 \times79$

To make a perfect cube we have to divide the number with 5×79=395.

Therefore, The least number is 395 by which 158000 should be divided to make it a perfect square.

(d) Find the square root of 211000 correct upto 2 decimal places.

We find the square root of 211000 by long division method.

Refer the attached figure below.

$\sqrt{211000}=459.34$

(e) Find the least number to be subtracted from 216000 to make it a perfect square.

First we find the square root of the number 216000.

The remainder while square root is being subtracted to find the square root.

1436 is the remainder which should be subtracted from 216000 to get a perfect square.

216000-1436=214564.

Therefore, 214564 is the least number to be subtracted from 216000 to make it a perfect square.