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Squares and Square Roots

Short Answer Type

41.

(–1) = 1. Is –1, a square root of 1?

(–2)² = 4. Is –2, a square root of 4?

(–9)² = 81. Is –9, a square root of 81?

133 Views

Long Answer Type

42.

By repeated subtraction of odd numbers starting from 1, find whether the following numbers are perfect squares or not? If the number is a perfect square, then find its square root.

(i) 121 (ii) 55 (iii) 36

(iv) 49 (v) 90

695 Views

Short Answer Type

43.

What could be the possible ‘one’s’ digits of the square root of each of the following numbers?

(i) 9801 (ii) 99856 (iii) 998001 (iv) 657666025

1005 Views

44.

Without doing any calculation, find the numbers which are surely not perfect squares.
(i) 152 (ii) 257 (iii) 408 (iv) 441

356 Views

45.

Find the square roots of 100 and 169 by the method of repeated subtraction.

946 Views

46.

Can we say that if a perfect square is of n-digits, then its square root will have $space space space space space n over 2$ digits if n is even of $space space space space space fraction numerator left parenthesis straight n plus 1 right parenthesis over denominator 2 end fraction$ if n is odd?

363 Views

47.

Without calculating square roots, find the number of digits in the square root of the following numbers.

(i) 25600 (ii) 100000000 (iii) 36864

750 Views

48.
Estimate the value of the following to the nearest whole number.

(i) $space space space space space space space square root of 80$ (ii) $space space space space space space square root of 1000$ (iii) $space space space space square root of 350$ (iv) $space space space space space square root of 500$

(i) $space space space square root of 80$

∵ 10²= 100, 9²= 81, 8²= 64
and 80 is between 64 and 81.
i.e. 64 < 80 < 81
or 8²< 80 < 9²

or $space space space space space space space 8 space less than space square root of 80 less than 9$

Thus, $space space space space space space square root of 80$ lies between 8 and 9.

(ii)

space space space space space space space space space space space square root of 1000

We know that 30²= 900, 31²= 961, 32²= 1024

∴ 1000 lies between 961 and 1024.
i.e. 916 < 1000 < 1024
or 31²< 1000 < 32²

or $space space space space space space space space space space space space 31 space less than space square root of 1000 less than 32$

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We have 18²= 324, 19²= 361

Since, 350 lies between 324 and 316.
i.e. 324 < 350 < 361
or 18²< 350 < 19²

or $space space space space space space space space space space space space space space space 18 less than square root of 350 less than 19$

Thus, $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ lies between 18 and 19.

(iv) $space space space space space space space space space space space square root of 500$

∵ 22²= 484 and 23²= 529
Since. 500 lies between 484 and 529
i.e. 484 < 500 < 529
or 22²< 500 < 23²

or $space space space space space space space space space space space space 22 space less than space square root of 500 less than 23$

Thus, $space space space space space space space space space space square root of 500$ lies between 22 and 23.